diffeomorphism
21Lie group — Lie groups …
22Horseshoe map — In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Smale while studying the behavior of the… …
23Schoen-Yau conjecture — In mathematics, the Schoen Yau conjecture is a disproved conjecture in hyperbolic geometry, named after the mathematicians Richard Schoen and Shing Tung Yau.It was inspired by a theorem of Erhard Heinz (1952). One method of disproof is the use of …
24Pullback (differential geometry) — Suppose that φ : M → N is a smooth map between smooth manifolds M and N ; then there is an associated linear map from the space of 1 forms on N (the linear space of sections of the cotangent bundle) to the space of 1 forms on M . This linear map… …
25Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …
26Augustin Banyaga — (b. March 31, 1947 in Kigali, Rwanda) is a Rwandan born American mathematician whose research fields include symplectic topology and contact geometry. He is currently a Professor of Mathematics at Pennsylvania State University.BiographyBanyaga… …
27Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …
28Differential topology — In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.… …
29Differential geometry — A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines. Differential geometry is a mathematical discipline that uses the techniques of differential and integral calculus, as well as… …
30Gravitational singularity — General relativity Introduction Mathematical formulation Resources Fundamental concepts …
