tangent manifold
1Tangent (disambiguation) — Tangent may refer to:In mathematics:* Tangent, in geometry, the straight line with the same direction as a curve at a given point, or analogous concepts for surfaces and higher dimensional smooth manifolds, such as the tangent space * One of the… …
2Tangent space — In mathematics, the tangent space of a manifold is a concept which facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector pointing from… …
3Tangent bundle — In mathematics, the tangent bundle of a smooth (or differentiable) manifold M , denoted by T ( M ) or just TM , is the disjoint unionThe disjoint union assures that for any two points x 1 and x 2 of manifold M the tangent spaces T 1 and T 2 have… …
4Manifold — 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),… …
5Tangent cone — In geometry, the tangent cone is a generalization of the notion of the tangent space to a manifold to the case of certain spaces with singularities. Definition in convex geometry Let K be a closed convex subset of a real vector space V and part;… …
6Tangent — For the tangent function see trigonometric functions. For other uses, see tangent (disambiguation). In geometry, the tangent line (or simply the tangent) to a curve at a given point is the straight line that just touches the curve at that point… …
7Tangent measure — In measure theory, tangent measures are used to study the local behavior of Radon measures, in much the same way as tangent spaces are used to study the local behavior of differentiable manifolds. Tangent measures are a useful tool in geometric… …
8Tangent vector — A tangent vector is a vector that follows the direction of a curve or a surface at a given point.* Differential geometry of curves, description in the context of curves in R n . * Tangent space, a general notion in the theory of manifolds …
9Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …
10Riemannian manifold — In Riemannian geometry, a Riemannian manifold ( M , g ) (with Riemannian metric g ) is a real differentiable manifold M in which each tangent space is equipped with an inner product g in a manner which varies smoothly from point to point. The… …
