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Complex vector bundle on a complex manifold
In mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifold X such that the total space E is a complex manifold and
Holomorphic_vector_bundle
Mathematical parametrization of vector spaces by another space
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space
Vector_bundle
vector bundle is a (holomorphic or algebraic) vector bundle that is stable in the sense of geometric invariant theory. Any holomorphic vector bundle may
Stable_vector_bundle
complex vector bundle is canonically oriented; in particular, one can take its Euler class. A complex vector bundle is a holomorphic vector bundle if X {\displaystyle
Complex_vector_bundle
complex geometry, the holomorphic tangent bundle of a complex manifold M {\displaystyle M} is the holomorphic analogue of the tangent bundle of a smooth manifold
Holomorphic_tangent_bundle
Mathematical theory
Chern–Weil theory that computes topological invariants of vector bundles and principal bundles on a smooth manifold M in terms of connections and curvature
Chern–Weil_homomorphism
Correspondsnce between Higgs bundles and fundamental group representations
{\displaystyle (E,\Phi )} where E → X {\displaystyle E\to X} is a holomorphic vector bundle and Φ : E → E ⊗ Ω 1 {\displaystyle \Phi :E\to E\otimes {\boldsymbol
Nonabelian Hodge correspondence
Nonabelian_Hodge_correspondence
connection) is a Chern connection associated to an inner product on a holomorphic vector bundle over a Kähler manifold that satisfies an analogue of Einstein's
Hermitian Yang–Mills connection
Hermitian_Yang–Mills_connection
Type of vector bundle
In mathematics, a Higgs bundle is a pair ( E , φ ) {\displaystyle (E,\varphi )} consisting of a holomorphic vector bundle E and a Higgs field φ {\displaystyle
Higgs_bundle
Study of complex manifolds and several complex variables
functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves. Application of transcendental
Complex_geometry
Vector bundles theorem
applied this new theory vector bundles to develop a notion of slope stability. Define the degree of a holomorphic vector bundle E → ( X , ω ) {\displaystyle
Kobayashi–Hitchin correspondence
Kobayashi–Hitchin_correspondence
Study of vector bundles, principal bundles, and fibre bundles
gauge theory is the general study of connections on vector bundles, principal bundles, and fibre bundles. Gauge theory in mathematics should not be confused
Gauge_theory_(mathematics)
On the Euler characteristic of a holomorphic vector bundle on a compact complex manifold
Hirzebruch–Riemann–Roch theorem applies to any holomorphic vector bundle E on a compact complex manifold X, to calculate the holomorphic Euler characteristic of E in sheaf
Hirzebruch–Riemann–Roch theorem
Hirzebruch–Riemann–Roch_theorem
Tangent spaces of a manifold
tangent bundle of a differentiable manifold M {\displaystyle M} is a manifold T M {\displaystyle TM} which assembles all the tangent vectors in M {\displaystyle
Tangent_bundle
In mathematics, vector bundles on algebraic curves may be studied as holomorphic vector bundles on compact Riemann surfaces, which is the classical approach
Vector bundles on algebraic curves
Vector_bundles_on_algebraic_curves
Mathematical technique for vector bundles
technique used to reduce questions about vector bundles to the case of line bundles. In the theory of vector bundles, one often wishes to simplify computations
Splitting_principle
System of partial differential equations used in Higgs field theory
{\displaystyle \Sigma } . A pair consisting of a holomorphic vector bundle E {\displaystyle E} with a holomorphic endomorphism-valued ( 1 , 0 ) {\displaystyle
Hitchin's_equations
Vector bundle of rank 1
tangent bundle is a way of organising these. More formally, in algebraic topology and differential topology, a line bundle is defined as a vector bundle of
Line_bundle
Generalizes the Kodaira vanishing theorem for ample vector bundle
on vector bundles. The theorem states the following Le Potier (1975): Let X be a n-dimensional compact complex manifold and E a holomorphic vector bundle
Le_Potier's_vanishing_theorem
Hermitian metrics on a holomorphic vector bundle. In particular, if the base manifold is Kähler and the vector bundle is its tangent bundle, then the Chern connection
Hermitian_connection
{\displaystyle {\mathcal {M}}_{g}} is the space of holomorphic differentials on the curve C. To define the Hodge bundle, let π : C g → M g {\displaystyle \pi \colon
Hodge_bundle
Concept in algebraic geometry
canonical bundle is anti-ample Matsusaka's big theorem Divisorial scheme: a scheme admitting an ample family of line bundles Holomorphic vector bundle Kodaira
Ample_line_bundle
Theorem in algebraic geometry
same duality statement for X a compact complex manifold and E a holomorphic vector bundle. Here, the Serre duality theorem is a consequence of Hodge theory
Serre_duality
Classifies holomorphic vector bundles over the complex projective line
Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic vector bundle over C P 1 {\displaystyle
Birkhoff–Grothendieck_theorem
Mathematic theorem about Riemann surfaces
theorem, proved by Narasimhan and Seshadri (1965), says that a holomorphic vector bundle over a compact Riemann surface is stable if and only if it comes
Narasimhan–Seshadri_theorem
Generalization of vector bundles
information. Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they form an abelian category, and so they are closed under
Coherent_sheaf
associated bundle E = P × GL ( n , C ) C n {\displaystyle E=P\times _{\operatorname {GL} (n,\mathbb {C} )}\mathbb {C} ^{n}} . This is a holomorphic vector bundle
Stable_principal_bundle
Concept in algebraic geometry
bundle Ω {\displaystyle \Omega } on V {\displaystyle V} . Over the complex numbers, it is the determinant bundle of the holomorphic cotangent bundle T
Canonical_bundle
Indian mathematician (1932–2021)
equations. He was a pioneer in the study of moduli spaces of holomorphic vector bundles on projective varieties. His work is considered the foundation
M._S._Narasimhan
Mathematical term
{\partial }}:\Omega ^{p,q-1}\to \Omega ^{p,q})}}.} If E is a holomorphic vector bundle on a complex manifold X, then one can define likewise a fine resolution
Dolbeault_cohomology
Algebraic variety in a projective space
the theory of holomorphic vector bundles (more generally coherent analytic sheaves) on X coincide with that of algebraic vector bundles. Chow's theorem
Projective_variety
Term in mathematics
every holomorphic vector bundle, and in particular every holomorphic line bundle, on this Riemann surface X is trivial. In particular, every line bundle is
Stein_manifold
Concept in differential geometry
d{\bar {z}}^{n}.} One can also consider a hermitian metric on a holomorphic vector bundle. The most important class of Hermitian manifolds are Kähler manifolds
Hermitian_manifold
Generalizes the Kodaira vanishing theorem
Kodaira vanishing theorem. Given a compact complex manifold M with a holomorphic line bundle F over M, the Nakano vanishing theorem provides a condition on
Nakano_vanishing_theorem
Mathematical result in differential geometry
(complex) dimension n with a holomorphic vector bundle V. We let the vector bundles E and F be the sums of the bundles of differential forms with coefficients
Atiyah–Singer_index_theorem
Japanese mathematician
notable for having proved that a hermitian–Einstein metric on a holomorphic vector bundle over a compact Kähler manifold has deep algebro-geometric implications
Shoshichi_Kobayashi
Type of mathematical functions
Röhrl (1956), states moreover that every holomorphic vector bundle on X is trivial. In particular, every line bundle is trivial, so H 1 ( X , O X ∗ ) = 0
Function of several complex variables
Function_of_several_complex_variables
Concept in algebraic geometry
same (finite) dimension. (Serre also proved Serre duality for holomorphic vector bundles on any compact complex manifold.) Grothendieck duality theory
Coherent_sheaf_cohomology
Manifold
any noncritical value of a holomorphic map. Smooth complex algebraic varieties are complex manifolds, including: Complex vector spaces. Complex projective
Complex_manifold
Chinese-American mathematician (born 1949)
of complex dimension two, a holomorphic vector bundle admits a hermitian Yang–Mills connection if and only if the bundle is stable. A result of Yau and
Shing-Tung_Yau
holomorphic vector bundle over a compact Kähler manifold. In particular let ( E , h ) {\displaystyle (E,h)} be a Hermitian holomorphic vector bundle over
Kähler_identities
Differential form on a manifold which is permitted to have complex coefficients
direct sum decomposition is stable under holomorphic coordinate changes, it also determines a vector bundle decomposition. In particular, for each k and
Complex_differential_form
British-Lebanese mathematician (1929–2019)
topological and holomorphic vector bundles on projective space. They solved the simplest unknown case, by showing that all rank 2 vector bundles over projective
Michael_Atiyah
Commutative algebra theorem
smooth vector bundles. The Oka-Grauert principle gives a bijection between isomorphism classes of topological and holomorphic vector bundles on affine
Quillen–Suslin_theorem
Concept in mathematics
correspondence. On the other hand, if we work with holomorphic (rather than algebraic) vector bundles with flat connection on a noncompact complex manifold
Riemann–Hilbert correspondence
Riemann–Hilbert_correspondence
principal fiber bundle reduces to Γ(A), the structure group of A. The corresponding holomorphic vector bundle with fibre A is the tangent bundle of the complex
Mutation_(Jordan_algebra)
Manifold upon which it is possible to perform calculus
principal bundle made up of the set of all frames over M. The frame bundle is useful because tensor fields on M can be regarded as equivariant vector-valued
Differentiable_manifold
Mathematical theory
addition, he equips these Riemann surfaces with Hermitian metrics on holomorphic vector bundles over X(C), the complex points of X {\displaystyle X} . This extra
Arakelov_theory
Partial differential equations whose solutions are instantons
system of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations of
Yang–Mills_equations
Type of metric in Riemannian geometry
metric on any holomorphic vector bundle over X {\displaystyle X} (note that the Levi-Civita connection on the holomorphic tangent bundle is precisely the
Kähler–Einstein_metric
bijection between instantons on complexified Minkowski space and holomorphic vector bundles on twistor space, which as a complex manifold is P 3 {\displaystyle
Twistor_correspondence
Relation between genus, degree, and dimension of function spaces over surfaces
holomorphic line bundles on a Riemann surface, the theorem can also be stated in a different, yet equivalent way: let L be a holomorphic line bundle on
Riemann–Roch_theorem
Space in mathematics and theoretical physics
vector bundles with self-dual connections on R 4 {\displaystyle \mathbb {R} ^{4}} (instantons) correspond bijectively to holomorphic vector bundles on
Twistor_space
square of the holomorphic cotangent bundle. If the section is holomorphic, then the quadratic differential is said to be holomorphic. The vector space of holomorphic
Quadratic_differential
Sheaf consisting of modules on a ringed space; generalizing vector bundles
consider D, the sheaf of differential operators.) fractional ideal holomorphic vector bundle generic freeness Vakil, Math 216: Foundations of algebraic geometry
Sheaf_of_modules
Concept in algebraic geometry
Jean-Pierre Demailly, Thomas Peternell and Michael Schneider, a holomorphic line bundle L on X is said to be nef if for every ϵ > 0 {\displaystyle \epsilon
Nef_line_bundle
for Science Awardee. Pioneer in the study of moduli spaces of holomorphic vector bundles on projective varieties P. T. Narasimhan pioneer of computational
List_of_Iyengars
Basic result in the representation theory of Lie groups
from holomorphic sections of certain complex vector bundles, and, more generally, from higher sheaf cohomology groups associated to such bundles. It is
Borel–Weil–Bott_theorem
Branch of mathematics
complex algebraic varieties, and complex analytic varieties, and holomorphic vector bundles and coherent sheaves over these spaces. Special examples of spaces
Geometry
Characteristic classes of vector bundles
the Chern classes are characteristic classes associated with complex vector bundles. They have since become fundamental concepts in many branches of mathematics
Chern_class
Theory proposed by Roger Penrose
P T {\displaystyle \mathbb {PT} } , and the latter to certain holomorphic vector bundles over regions in P T {\displaystyle \mathbb {PT} } . These constructions
Twistor_theory
Smooth manifold
J^{2}=-1} when regarded as a vector bundle isomorphism J : T M → T M {\displaystyle J\colon TM\to TM} on the tangent bundle. A manifold equipped with an
Almost_complex_manifold
Algebro-geometric stability condition
holomorphic vector bundle is equivalent to its stability. Yau suggested this stability condition should be an analogue of slope stability of vector bundles
K-stability
Concept in differential geometry
holonomy of connections in vector bundles, holonomy of Cartan connections, and holonomy of connections in principal bundles. In each of these cases, the
Holonomy
Differentiable manifold
{C} ^{2}} . The holomorphic tangent bundle of C 2 {\displaystyle \mathbb {C} ^{2}} consists of all linear combinations of the vectors ∂ ∂ z , ∂ ∂ w .
CR_manifold
Analytic function on the upper half-plane with a certain behavior under the modular group
G, that is holomorphic on H and at all cusps of G. Again, modular forms that vanish at all cusps are called cusp forms for G. The C-vector spaces of modular
Modular_form
Meromorphic differential form
\cdots \oplus {\mathcal {O}}_{X}dz_{n}.} This describes the holomorphic vector bundle Ω X 1 ( log D ) {\displaystyle \Omega _{X}^{1}(\log D)} on X
Logarithmic_form
introduced by Ward (1977), that (among other things) relates holomorphic vector bundles on 3-dimensional complex projective space CP3 to solutions of
Penrose_transform
Swedish mathematician
results for the curvature of holomorphic vector bundles naturally associated to holomorphic fibrations. These vector bundles arise as the zeroth direct
Bo_Berndtsson
Hungarian-American mathematician (1923-2005)
via holomorphic sheaves and their cohomology groups; and for work on foliations. With Chern he worked on Nevanlinna theory, studied holomorphic vector bundles
Raoul_Bott
Property of a differential manifold that includes complex structures
bundle. (n, 0)-forms are pure spinors, as they are annihilated by antiholomorphic tangent vectors and by holomorphic one-forms. Thus this line bundle
Generalized_complex_structure
On finding a maximal set of solutions of a system of first-order homogeneous linear PDEs
foliation by maximal integral manifolds whose tangent bundles are spanned by the given vector fields. The theorem generalizes the existence theorem for
Frobenius theorem (differential topology)
Frobenius_theorem_(differential_topology)
Type of Riemannian manifold
manifold ( M , I ) {\displaystyle (M,I)} , is holomorphically symplectic (equipped with a holomorphic, non-degenerate, closed 2-form). More precisely
Hyperkähler_manifold
Theorem about complex manifolds
matrix of the holomorphic tangent bundle Atiyah–Bott fixed-point theorem Holomorphic Lefschetz fixed-point formula Bott, Raoul (1967), "Vector fields and
Bott_residue_formula
Jacobian Theorem of the cube Selmer group Michael Atiyah classifies holomorphic vector bundles on an elliptic curve 1961 Goro Shimura and Yutaka Taniyama, Complex
Timeline_of_abelian_varieties
In algebraic geometry, the Iitaka dimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective
Iitaka_dimension
Degree of differentiability of a function or map
p}:T_{p}M\to T_{F(p)}N,} and on the level of the tangent bundle, the pushforward is a vector bundle homomorphism: F ∗ : T M → T N . {\displaystyle F_{*}:TM\to
Smoothness
English mathematician (born 1957)
This contrasts with the situation in higher dimensions. A stable holomorphic vector bundle over a non-singular projective algebraic variety admits a Hermitian–Einstein
Simon_Donaldson
Manifold with Riemannian, complex and symplectic structure
Equivalently, X {\displaystyle X} is projective if and only if there is a holomorphic line bundle L {\displaystyle L} on X {\displaystyle X} with a hermitian metric
Kähler_manifold
Kind of complex manifold
particular complex tori, there is a construction relating the holomorphic line bundles L → X {\displaystyle L\to X} whose pullback π ∗ L → X ~ {\displaystyle
Complex_torus
Tool in algebraic topology
importance. For example, an algebraic vector bundle (on a locally Noetherian scheme) or a holomorphic vector bundle (on a complex analytic space) can be
Sheaf_cohomology
Theorem in algebraic geometry
4171/114-1/14. ISBN 978-3-03719-114-9. Bogomolov, F. A. (1979). "Holomorphic Tensors and Vector Bundles on Projective Varieties". Izvestiya Akademii Nauk SSSR.
Bogomolov–Sommese vanishing theorem
Bogomolov–Sommese_vanishing_theorem
Mathematical structure in differential geometry
π ♯ : T ∗ M → T M {\displaystyle \pi ^{\sharp }:T^{*}M\to TM} is a vector bundle isomorphism. Nondegenerate Poisson bivector fields are actually the
Poisson_manifold
Metric on a determinant line bundle
correspondence. The Quillen metric is primarily considered in the study of holomorphic vector bundles over Riemann surfaces or higher dimensional complex manifolds
Quillen_metric
Topics referred to by the same term
a holomorphic vector bundle with a Hermitian structure, is the unique metric connection D, such that the part which increases the anti-holomorphic type
Canonical_connection
In mathematics, convenient vector spaces are locally convex vector spaces satisfying a very mild completeness condition. Traditional differential calculus
Convenient_vector_space
Tool to track locally defined data attached to the open sets of a topological space
complex vector bundles, or vector bundles in algebraic geometry (where O {\displaystyle {\mathcal {O}}} consists of smooth functions, holomorphic functions
Sheaf_(mathematics)
Superconductivity theory
ISSN 0010-3616. S2CID 122086974. Bradlow, Steven B. (1990). "Vortices in holomorphic line bundles over closed Kähler manifolds". Communications in Mathematical Physics
Ginzburg–Landau_theory
normal cone to Z ↪ X {\displaystyle Z\hookrightarrow X} . For a holomorphic vector bundle E {\displaystyle E} over a complex manifold M {\displaystyle M}
Segre_class
On self-duality of differential equations
equations. Via the Penrose–Ward transform these solutions give the holomorphic vector bundles often seen in the context of algebraic integrable systems. Ablowitz
Ward's_conjecture
Model of the extended complex plane plus a point at infinity
example, any rational function on the complex plane can be extended to a holomorphic function on the Riemann sphere, with the poles of the rational function
Riemann_sphere
Module over a sheaf of differential operators
of the differential equation P f = 0, where f is some holomorphic function in C, say. The vector space consisting of the solutions of that equation is
D-module
Topological space that locally resembles Euclidean space
what a tangent vector might be, and there is no intrinsic notion of a normal bundle, but instead there is an intrinsic stable normal bundle. The n-sphere
Manifold
Math/physics concept
group reduces to the spin group. Holomorphic tangent bundles on CR manifolds. In general, let E be a given vector bundle of fibre dimension k and G ⊂ GL(k)
Connection_form
Field theory involving topological effects in physics
the theory is the number of pseudo holomorphic maps f : M → X in the sense of Gromov (they are ordinary holomorphic maps if X is a Kähler manifold). If
Topological quantum field theory
Topological_quantum_field_theory
Group that is also a differentiable manifold with group operations that are smooth
( 2 , C ) {\displaystyle \operatorname {SL} (2,\mathbb {C} )} ), and holomorphic maps. Similarly, using an alternate metric completion of Q {\displaystyle
Lie_group
Normed vector space that is complete
normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is
Banach_space
on the moduli stack of vector bundles on a curve" (PDF), in Schmitt, Alexander (ed.), Affine flag manifolds and principal bundles, Trends in Mathematics
Moduli stack of principal bundles
Moduli_stack_of_principal_bundles
Penrose–Ward transform they can therefore be interpreted in terms of holomorphic vector bundles on complex manifolds called twistor spaces. This allows the use
Isomonodromic_deformation
with all holomorphic Killing vectors on the cone and in particular with all isometries of the Sasakian manifold. If the orbits of the vector field close
Sasakian_manifold
HOLOMORPHIC VECTOR-BUNDLE
HOLOMORPHIC VECTOR-BUNDLE
Boy/Male
American, British, Christian, Danish, Dutch, English, Finnish, French, German, Greek, Hindu, Indian, Irish, Jamaican, Latin, Romanian, Slovenia, Spanish, Swedish, Swiss, Tamil, Ukrainian
Victorious; Conqueror; Winner; Champion; One who Conquers; Victory
Boy/Male
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Greek, Italian, Latin, Portuguese, Shakespearean, Spanish
Steadfast; Anchor; Holds Fast; Star; Coined from Esther Vanhomrigh; Tenacious; Defend; Hold Fast; Coined from Esther Vanho
Boy/Male
Christian & English(British/American/Australian)
Steadfast
Male
English
Short form of English Sylvester, VESTER means "from the forest."
Male
English
Roman Latin name VICTOR means "conqueror."Â
Male
Russian
(Cyrillic Виктор): Slavic form of Roman Latin Victor, VIKTOR means "conqueror." In use by the Bulgarians, Russians and Serbians. Compare with another form of Viktor.
Male
Portuguese
Galician-Portuguese form of Roman Latin Victor, VITOR means "conqueror."
Boy/Male
Australian, Basque, Czech, Czechoslovakian, Danish, Finnish, French, German, Hungarian, Latin, Polish, Slovenia, Swedish, Swiss, Ukrainian
The Conqueror; Victory; Victorious; Conquer
Surname or Lastname
Scottish
Scottish : Anglicized form of the Gaelic personal name Eachann (earlier Eachdonn, already confused with Norse Haakon), composed of the elements each ‘horse’ + donn ‘brown’.English : found in Yorkshire and Scotland, where it may derive directly from the medieval personal name. According to medieval legend, Britain derived its name from being founded by Brutus, a Trojan exile, and Hector was occasionally chosen as a personal name, as it was the name of the Trojan king’s eldest son. The classical Greek name, HektÅr, is probably an agent derivative of Greek ekhein ‘to hold back’, ‘hold in check’, hence ‘protector of the city’.German, French, and Dutch : from the personal name (see 2 above). In medieval Germany, this was a fairly popular personal name among the nobility, derived from classical literature. It is a comparatively rare surname in France.
Male
Greek
(á¼ÎºÏ„ωÏ) Variant spelling of Greek Hektor, EKTOR means "defend; hold fast."
Boy/Male
Christian & English(British/American/Australian)
Conqueror
Boy/Male
Arthurian Legend
Father of Arthur.
Male
Portuguese
Portuguese form of Latin Hector, HEITOR means "defend; hold fast."
Male
English
 Anglicized form of Scottish Gaelic Eachann, HECTOR means "brown horse." Compare with another form of Hector.
Boy/Male
Spanish American Shakespearean Greek Latin
Tenacious.
Boy/Male
English American
Doctor; teacher.
Boy/Male
Spanish
Victor.
Male
Arthurian
, sir Hector de Maris; (defender).
Male
Scandinavian
 Scandinavian form of Roman Latin Victor, VIKTOR means "conqueror." Compare with another form of Viktor.
Boy/Male
Latin American Spanish
Conqueror.
HOLOMORPHIC VECTOR-BUNDLE
HOLOMORPHIC VECTOR-BUNDLE
Boy/Male
Arabic
Good News; Glad Tiding
Boy/Male
Tamil
The best
Boy/Male
English
Foreigner.
Girl/Female
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Wonderful
Boy/Male
Latin
Friend of Hercules.
Girl/Female
Hindu
Combination of Lord Shiva and Parvati
Girl/Female
Irish Celtic
noble.
Girl/Female
Muslim
Fair complexion (Name of the wife of the prophet)
Girl/Female
Afghan, Arabic, Celebrity, Greek, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Punjabi, Sikh, Telugu, Traditional
Beauty and Happiness of Home; Beauty; Decoration; Delicate; Honor
Girl/Female
Hindu, Indian, Tamil
Beauty of Flower
HOLOMORPHIC VECTOR-BUNDLE
HOLOMORPHIC VECTOR-BUNDLE
HOLOMORPHIC VECTOR-BUNDLE
HOLOMORPHIC VECTOR-BUNDLE
HOLOMORPHIC VECTOR-BUNDLE
n.
A term made up of the two parts / + /1 /-1, where / and /1 are vectors.
a.
Of or pertaining to victory, or a victor' being a victor; bringing or causing a victory; conquering; winning; triumphant; as, a victorious general; victorious troops; a victorious day.
n.
Any mechanical contrivance intended to remedy a difficulty or serve some purpose in an exigency; as, the doctor of a calico-printing machine, which is a knife to remove superfluous coloring matter; the doctor, or auxiliary engine, called also donkey engine.
n.
A mathematical instrument, consisting of two rulers connected at one end by a joint, each arm marked with several scales, as of equal parts, chords, sines, tangents, etc., one scale of each kind on each arm, and all on lines radiating from the common center of motion. The sector is used for plotting, etc., to any scale.
a.
Pertaining to a rector or a rectory; rectoral.
v. t.
To tamper with and arrange for one's own purposes; to falsify; to adulterate; as, to doctor election returns; to doctor whisky.
n.
A pregnant woman; a mother; as, A has a son B by one venter, and a daughter C by another venter; children by different venters.
n.
The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.
n.
The province of a rector; a parish church, parsonage, or spiritual living, with all its rights, tithes, and glebes.
n.
The turning factor of a quaternion.
n.
An astronomical instrument, the limb of which embraces a small portion only of a circle, used for measuring differences of declination too great for the compass of a micrometer. When it is used for measuring zenith distances of stars, it is called a zenith sector.
v. t.
To confer a doctorate upon; to make a doctor.
n.
A woman who wins a victory; a female victor.
a.
Of, pertaining to, or characterized by, trimorphism; -- contrasted with monomorphic, dimorphic, and polymorphic.
n.
A belly, or protuberant part; a broad surface; as, the venter of a muscle; the venter, or anterior surface, of the scapula.
n.
An African weaver bird (Textor alector).
n.
Same as Radius vector.
n.
A directed quantity, as a straight line, a force, or a velocity. Vectors are said to be equal when their directions are the same their magnitudes equal. Cf. Scalar.
n.
A contrivance for removing superfluous ink or coloring matter from a roller. See Doctor, 4.
n.
The chief elective officer of some universities, as in France and Scotland; sometimes, the head of a college; as, the Rector of Exeter College, or of Lincoln College, at Oxford.