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Branch of mathematics
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It
Differential_geometry
In classical differential geometry, development is the rolling of one smooth surface over another in Euclidean space. For example, the tangent plane to
Development (differential geometry)
Development_(differential_geometry)
Area of mathematics
Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there
Discrete differential geometry
Discrete_differential_geometry
This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. List of curves topics
List of differential geometry topics
List_of_differential_geometry_topics
Mathematics of smooth surfaces
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most
Differential geometry of surfaces
Differential_geometry_of_surfaces
Branch of differential geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds. An example of a Riemannian manifold is a surface, on which
Riemannian_geometry
Topics referred to by the same term
changed over time Sustainable development Development (differential geometry), rolling one smooth surface over another Development (drafting), a type of technical
Development
Technique in statistics
Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. It
Information_geometry
Mathematical notion of infinitesimal difference
mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. The term differential is used nonrigorously in calculus
Differential_(mathematics)
Branch of mathematics
methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc
Geometry
Study of complex manifolds and several complex variables
analysis. Complex geometry sits at the intersection of algebraic geometry, differential geometry, and complex analysis, and uses tools from all three areas
Complex_geometry
Study of angle-preserving transformations of a geometric space
conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry is
Conformal_geometry
Geometry without using coordinates
Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic
Synthetic_geometry
American mathematician and Nobel Laureate (1928–2015)
contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow game theorists John
John_Forbes_Nash_Jr.
In mathematics, stochastic analysis on manifolds or stochastic differential geometry is the study of stochastic analysis over smooth manifolds. It is
Stochastic analysis on manifolds
Stochastic_analysis_on_manifolds
Surface able to be flattened without distortion
such as ductwork to shipbuilding. Relatedly, in classical differential geometry, a development is the rolling of one smooth surface over another in Euclidean
Developable_surface
In mathematics, straight line touching a plane curve without crossing it
concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; . The word tangent comes from
Tangent
Mathematics award
Arroja Neves – "For outstanding contributions to several areas of differential geometry, including work on scalar curvature, geometric flows, and his solution
Breakthrough Prize in Mathematics
Breakthrough_Prize_in_Mathematics
References Absolute differential calculus An older name of Ricci calculus Absolute geometry Also called neutral geometry, a synthetic geometry similar to Euclidean
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
24 mathematical problems stated in 1982
Thurston's 24 questions are a set of mathematical problems in differential geometry posed by American mathematician William Thurston in his influential
Thurston's_24_questions
Branch of computer science
considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing
Computational_geometry
Type of geometry
projective algebraic geometry (the study of projective varieties) and projective differential geometry (the study of differential invariants of the projective
Projective_geometry
Branch of mathematics
Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics
Calculus
Mathematics of varieties with integer coordinates
geometry. The extensive development of algebraic geometry in the 20th century produced powerful tools to study these equations. Diophantine geometry is
Diophantine_geometry
Methods used to find numerical solutions of ordinary differential equations
methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).
Numerical methods for ordinary differential equations
Numerical_methods_for_ordinary_differential_equations
Brazilian mathematician
He spent most of his career at IMPA and is seen as the doyen of differential geometry in Brazil. Do Carmo studied civil engineering at the University
Manfredo_do_Carmo
French mathematician (1869–1951)
the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. He also made significant contributions
Élie_Cartan
Notion in calculus
twentieth-century developments in mathematical analysis and differential geometry, it became clear that the notion of the differential of a function could
Differential_of_a_function
Russian mathematician
he became a professor of Higher Geometry and Topology, and in 1992, was appointed as head of Differential Geometry and Applications in the Department
Anatoly_Fomenko
Object in differential geometry
In differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is a bilinear map of two input
Torsion_tensor
Norwegian mathematician (1842–1899)
applied it to the study of geometry and differential equations. He also made substantial contributions to the development of algebra. Marius Sophus Lie
Sophus_Lie
Italian-born American mathematician (1923–2023)
Mathematics at the University of Pennsylvania, specializing in differential geometry, partial differential equations and their applications. Calabi was born in
Eugenio_Calabi
Study of geometry using a coordinate system
foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system
Analytic_geometry
System of moving vectors in differential geometry
In differential geometry, parallel transport (or parallel translation) is a way of transporting geometrical data along smooth curves in a manifold. If
Parallel_transport
Study of rates of change
of mathematics, such as complex analysis, functional analysis, differential geometry, measure theory, and abstract algebra. The theory of derivatives
Differential_calculus
Construct allowing differentiation of tangent vector fields of manifolds
In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent
Affine_connection
Type of differential equation
also arise from many purely mathematical considerations, such as differential geometry and the calculus of variations; among other notable applications
Partial_differential_equation
Typically linear operator defined in terms of differentiation of functions
D_{n}^{b_{n}}} . In differential geometry and algebraic geometry it is often convenient to have a coordinate-independent description of differential operators between
Differential_operator
Generalization of affine connections
In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also
Cartan_connection
Italian mathematician (1835–1900)
1900) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity
Eugenio_Beltrami
Historical development of geometry
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry
History_of_geometry
Polish mathematician (1866–1953)
Żorawski's main interests were invariants of differential forms, integral invariants of Lie groups, differential geometry and fluid mechanics. His work in these
Kazimierz_Żorawski
Partial differential equation
In differential geometry and geometric analysis, the Ricci flow (/ˈriːtʃi/ REE-chee, Italian: [ˈrittʃi]), sometimes also referred to as Hamilton's Ricci
Ricci_flow
Branch of mathematics
space; this parallels developments in topology, differential and complex geometry. One key achievement of this abstract algebraic geometry is Grothendieck's
Algebraic_geometry
Manifold upon which it is possible to perform calculus
The study of calculus on differentiable manifolds is known as differential geometry. "Differentiability" of a manifold has been given several meanings
Differentiable_manifold
German mathematician (1826–1866)
who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first
Bernhard_Riemann
Non-Euclidean geometry
nineteenth century stimulated the development of non-Euclidean geometry generally, including hyperbolic geometry. Elliptic geometry has a variety of properties
Elliptic_geometry
Euclidean geometry without distance and angles
In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance
Affine_geometry
German mathematician and physicist (1829–1900)
physicist. He introduced fundamental concepts of differential geometry, opening the way for the development of tensor calculus, which would later provide
Elwin_Bruno_Christoffel
Chinese-American mathematician and poet
to differential geometry and topology. He has been called the "father of modern differential geometry" and is widely regarded as a leader in geometry and
Shiing-Shen_Chern
Concept in differential geometry
In differential geometry, a triply periodic minimal surface (TPMS) is a minimal surface in R 3 {\displaystyle \mathbb {R} ^{3}} that is invariant under
Triply periodic minimal surface
Triply_periodic_minimal_surface
Theoretical attempts to unify the forces of nature
two World Wars. This work spurred the purely mathematical development of differential geometry. This article describes various attempts at formulating a
Classical unified field theories
Classical_unified_field_theories
Chinese-American mathematician (born 1949)
Yau is considered one of the major contributors to the development of modern differential geometry and geometric analysis. The impact of Yau's work are
Shing-Tung_Yau
American mathematician (1943–2024)
Hamilton's mathematical contributions are primarily in the field of differential geometry and more specifically geometric analysis. He is best known for having
Richard_S._Hamilton
Mathematical physics relation
back-and-forth translation between the concepts of gauge theory and those of differential geometry. The dictionary appeared in 1975 in an article by Tai Tsun Wu and
Wu–Yang_dictionary
American mathematician and mathematical physicist (1931–2020)
1975 The Development of mathematics in the 19th Century, 1979 Geometry of Riemannian Spaces, 1983 The geometric theory of ordinary differential equations
Robert Hermann (mathematician)
Robert_Hermann_(mathematician)
On finding a maximal set of solutions of a system of first-order homogeneous linear PDEs
manifolds. The theorem is foundational in differential topology and calculus on manifolds. Contact geometry studies 1-forms that maximally violate the
Frobenius theorem (differential topology)
Frobenius_theorem_(differential_topology)
Type of non-Euclidean geometry
mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate
Hyperbolic_geometry
Russian mathematician (born 1936)
born 21 June 1936) is a Russian mathematician. He works in differential and convex geometry. Burago studied at Leningrad University, where he obtained
Yuri_Burago
Intrinsic geometric structures in mathematics
in the 1950s. The classical nineteenth century approach to the differential geometry of surfaces, due in large part to Carl Friedrich Gauss, has been
Riemannian connection on a surface
Riemannian_connection_on_a_surface
American mathematician (1911–1999)
important contributions to the early development of general relativity, as well as differential geometry and differential equations. Taub graduated in 1931
Abraham_H._Taub
Topological space that locally resembles Euclidean space
systematic treatment of the theory of manifolds, Riemannian geometry, classical differential geometry, and numerous other topics at the first- and second-year
Manifold
In differential geometry, the Carathéodory conjecture is a mathematical conjecture attributed to Constantin Carathéodory by Hans Ludwig Hamburger in a
Carathéodory_conjecture
Branch of mathematics
combinatorics Continuous probability Differential entropy in information theory Differential games Differential geometry, the application of calculus to specific
Mathematical_analysis
Branch of algebraic geometry
arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around
Arithmetic_geometry
American mathematician
September 8, 1961) is an American mathematician specializing in differential geometry and gauge theory. He is the Singer Professor of Mathematics and
Tomasz_Mrowka
Geometric system with a finite number of points
A finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean
Finite_geometry
Parzygnat has a detailed development of this framework. An alternative approach, motivated by the goal of constructing geometry over spaces of paths and
Higher_gauge_theory
Affine connection on the tangent bundle of a manifold
In Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine
Levi-Civita_connection
In differential geometry, the F {\displaystyle F} -Yang–Mills equations (or F {\displaystyle F} -YM equations) are a generalization of the Yang–Mills
F-Yang–Mills_equations
Two geometries based on axioms closely related to those specifying Euclidean geometry
non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the
Non-Euclidean_geometry
Mathematical measure of how much a curve twists
"Torsion". mathworld.wolfram.com. Pressley, Andrew (2001), Elementary Differential Geometry, Springer Undergraduate Mathematics Series, Springer-Verlag, ISBN 1-85233-152-6
Torsion_of_a_curve
Field of knowledge
Calculus, consisting of the two subfields differential calculus and integral calculus, originated with geometry but evolved into the study of continuous
Mathematics
Mathematical structure in differential geometry
In differential geometry, a field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold
Poisson_manifold
Mathematical model of the physical space
Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements
Euclidean_geometry
Study of discrete mathematical structures
calculus, discrete Fourier transforms, discrete geometry, discrete logarithms, discrete differential geometry, discrete exterior calculus, discrete Morse
Discrete_mathematics
In differential geometry, the Bi-Yang–Mills equations (or Bi-YM equations) are a modification of the Yang–Mills equations. Its solutions are called Bi-Yang–Mills
Bi-Yang–Mills_equations
Vector bundles theorem
In differential geometry, algebraic geometry, and gauge theory, the Kobayashi–Hitchin correspondence (or Donaldson–Uhlenbeck–Yau theorem) relates stable
Kobayashi–Hitchin correspondence
Kobayashi–Hitchin_correspondence
Field theory involving topological effects in physics
Witten, Edward (1982). "Super-symmetry and Morse Theory". Journal of Differential Geometry. 17 (4): 661–692. doi:10.4310/jdg/1214437492. Witten, Edward (1988a)
Topological quantum field theory
Topological_quantum_field_theory
Russian-French mathematician
immersions and similar objects in symplectic and contact geometry. His well-known book Partial Differential Relations collects most of his work on these problems
Mikhael Gromov (mathematician)
Mikhael_Gromov_(mathematician)
American mathematician (born 1943)
California, Berkeley, working in the field of differential geometry, and especially in Poisson geometry. Weinstein was born in New York City. After attending
Alan_Weinstein
Class of mathematical software
differentiable manifolds. EDC and RGTC, "Exterior Differential Calculus" and "Riemannian Geometry & Tensor Calculus," are free Mathematica packages for
Tensor_software
Mathematical methods that avoid coordinates
with coordinate-free treatments include vector calculus, tensors, differential geometry, and computer graphics. In physics, the existence of coordinate-free
Coordinate-free
Swiss-Hungarian mathematician (1878–1936)
of physics at the Zurich Polytechnic. Grossmann was an expert in differential geometry and tensor calculus, the mathematical tools which would provide
Marcel_Grossmann
Type of group in group theory
examples of Riemannian manifolds and hence are objects of interest in differential geometry and topology. Finally, these two topics join in the theory of automorphic
Arithmetic_group
Geometry without the parallel postulate
Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally
Absolute_geometry
Mathematical notation used for calculus
related notation involving the same differentials, a notation whose efficiency proved decisive in the development of continental European mathematics
Leibniz's_notation
Differentiable manifold
MR 0425012. Gromov, Mikhail (1978). "Almost flat manifolds". Journal of Differential Geometry. 13 (2): 231–241. doi:10.4310/jdg/1214434488. MR 0540942. Chow,
Nilmanifold
Russian and Canadian mathematician (born 1947)
algebraic geometry, commutative algebra, singularity theory, differential geometry and differential equations. His research is in the development of the
Askold_Khovanskii
Russian mathematician (1937–2010)
theory, topology, real algebraic geometry, symplectic geometry, differential equations, classical mechanics, differential-geometric approach to hydrodynamics
Vladimir_Arnold
French mathematical physicist (1915–1998)
researchers recruited by this institution. Lichnerowicz studied differential geometry under Élie Cartan. His doctoral dissertation, completed in 1939
André_Lichnerowicz
Math/physics concept
specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms
Connection_form
Chinese mathematician
Chinese mathematician, educator and poet. He was the founder of differential geometry in China, and served as president of Fudan University and honorary
Su_Buqing
Study of vector bundles, principal bundles, and fibre bundles
In mathematics, and especially differential geometry and mathematical physics, gauge theory is the general study of connections on vector bundles, principal
Gauge_theory_(mathematics)
Theory proposed by Roger Penrose
mathematical tools that have applications to differential and integral geometry, nonlinear differential equations and representation theory, and in physics
Twistor_theory
Technique to solve partial differential equations
neural networks (PINNs) to solve nonlinear partial differential equations on arbitrary complex-geometry domains. The XPINNs further push the boundaries of
Physics-informed neural networks
Physics-informed_neural_networks
like dimension. Outline of geometry Glossary of differential geometry and topology Glossary of Riemannian and metric geometry Glossary of scheme theory
Lists_of_mathematics_topics
Branch of geometry
geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational geometry
Convex_geometry
German-born American mathematician (1924–2021)
and educator, who has contributed to knowledge in differential geometry, topology, algebraic geometry, and convexity. He was Jewish and has also contributed
Heinrich_Guggenheimer
Geometric model of the physical space
for differential geometry. In the 19th century, developments of the geometry of three-dimensional space came with William Rowan Hamilton's development of
Three-dimensional_space
DEVELOPMENT DIFFERENTIAL-GEOMETRY
DEVELOPMENT DIFFERENTIAL-GEOMETRY
Girl/Female
Hindu, Indian
Development
Girl/Female
Muslim
Altitude, Height, High, Development
Boy/Male
Hindu
Development, Prosper
Boy/Male
Hindu, Indian
Development
Boy/Male
Tamil
Development, Prosper
Girl/Female
Hindu, Indian
Development; Improvement; Progress
Boy/Male
Tamil
Development, Expanding
Boy/Male
Arabic, Muslim, Sindhi
Dignity; Development
Boy/Male
Hindu, Indian, Tamil
Devlopment; Hope
Boy/Male
Hindu
Development, Prosper
Boy/Male
Tamil
Development or expanding
Boy/Male
Indian, Sanskrit
Development; Expansion
Boy/Male
Bengali, Indian
Development; Brightness
Boy/Male
Hindu
Development or expanding
Boy/Male
Bengali, Indian
Development of God
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Sindhi, Tamil, Telugu
Progress; Development; Improvement
Boy/Male
Hindu
Development, Expanding
Boy/Male
Tamil
Development, Prosper
Boy/Male
Indian
Altitude, Height, High, Development
Boy/Male
Muslim
Altitude, Height, High, Development
DEVELOPMENT DIFFERENTIAL-GEOMETRY
DEVELOPMENT DIFFERENTIAL-GEOMETRY
Boy/Male
American, Australian, French, German, Shakespearean, Spanish, Teutonic
Alfonso; Ready for Battle; Form of Alphonse
Boy/Male
Arabic, Muslim
Pillar; Prop; Support
Boy/Male
Tamil
Well recited
Girl/Female
Hindu
Equaled, Similar
Surname or Lastname
English (Lancashire)
English (Lancashire) : variant of Hesketh.
Surname or Lastname
English
English : variant of Pickerell.
Boy/Male
American, Anglo, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Irish, Latin, Netherlands, Swedish, Swiss, Teutonic
Free; Free Landholder; Javelin; Spear; Variant of Francis; French Man; A Man Form France
Girl/Female
Native American
Thunder.
Boy/Male
Teutonic American English German
Bear.
Boy/Male
Arabic, Muslim
Longing; Desirous
DEVELOPMENT DIFFERENTIAL-GEOMETRY
DEVELOPMENT DIFFERENTIAL-GEOMETRY
DEVELOPMENT DIFFERENTIAL-GEOMETRY
DEVELOPMENT DIFFERENTIAL-GEOMETRY
DEVELOPMENT DIFFERENTIAL-GEOMETRY
n.
The series of changes which animal and vegetable organisms undergo in their passage from the embryonic state to maturity, from a lower to a higher state of organization.
n.
The equivalent expression into which another has been developed.
n.
The act or process of changing or expanding an expression into another of equivalent value or meaning.
n.
One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
v. t.
To distinguish or mark by a specific difference; to effect a difference in, as regards classification; to develop differential characteristics in; to specialize; to desynonymize.
n.
An increment, usually an indefinitely small one, which is given to a variable quantity.
n.
A small difference in rates which competing railroad lines, in establishing a common tariff, allow one of their number to make, in order to get a fair share of the business. The lower rate is called a differential rate. Differentials are also sometimes granted to cities.
n.
The elaboration of a theme or subject; the unfolding of a musical idea; the evolution of a whole piece or movement from a leading theme or motive.
n.
A characteristic or essential attribute; a differential.
a.
Ready to obey; reverent; differential; also, servilely submissive.
n.
An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.
a.
Of or pertaining to a differential, or to differentials.
a.
Relating to or indicating a difference; creating a difference; discriminating; special; as, differential characteristics; differential duties; a differential rate.
a.
Pertaining to, or characteristic of, the process of development; as, the developmental power of a germ.
n.
The act of developing or disclosing that which is unknown; a gradual unfolding process by which anything is developed, as a plan or method, or an image upon a photographic plate; gradual advancement or growth through a series of progressive changes; also, the result of developing, or a developed state.
n.
A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
a.
Relating to differences of motion or leverage; producing effects by such differences; said of mechanism.
v. t.
To obtain the differential, or differential coefficient, of; as, to differentiate an algebraic expression, or an equation.
pl.
of Differentia
a.
That deduces; inferential.