Concept information
Preferred term
differential geometry
Definition(s)
-
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Differential_geometry)
Broader concept(s)
Narrower concept(s)
- arc length
- Atiyah-Singer index theorem
- Bäcklund transform
- Beez's theorem
- conformal geometry
- connection
- contact geometry
- cotangent bundle
- covariant derivative
- curve of pursuit
- differentiable manifold
- differential form
- differential geometry of curves
- differential geometry of surfaces
- exterior derivative
- Fenchel's theorem
- foliation
- four-vertex theorem
- Frobenius' theorem
- Hilbert's theorem
- Hitchin integrable system
- holonomy
- implicit function theorem
- inflection point
- interior product
- jet
- Lie derivative
- mapping class group
- parabolic geometry
- Poincaré-Hopf theorem
- prime decomposition theorem for 3-manifolds
- Riemannian geometry
- Schur's theorem
- sheaf
- singular point of a curve
- symplectic geometry
- systolic geometry
- tangent
- tangent bundle
- tangent line to a plane curve
- tangent space
- tensor
- tensor calculus
- vector calculus
- Willmore conjecture
In other languages
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French
URI
http://data.loterre.fr/ark:/67375/PSR-V0G085HP-P
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