tangent bundle

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• Tangent 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… …   Wikipedia

• Double tangent bundle — In mathematics, particularly differential topology, the double tangent bundle or the second tangent bundle refers to the tangent bundle (TTM,πTTM,TM) of the total space TM of the tangent bundle (TM,πTM,M) of a smooth manifold M [1]. The second… …   Wikipedia

• Unit tangent bundle — In mathematics, the unit tangent bundle of a Finsler manifold ( M , || . ||), denoted by UT( M ) or simply UT M , is a fiber bundle over M given by the disjoint union:mathrm{UT} (M) := coprod {x in M} left{ v in mathrm{T} {x} (M) left| | v | {x} …   Wikipedia

• Tangent 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… …   Wikipedia

• Bundle (mathematics) — In mathematics, a bundle is a generalization of a fiber bundle dropping the condition of a local product structure. The requirement of a local product structure rests on the bundle having a topology. Without this requirement, more general objects …   Wikipedia

• Vector bundle — The Möbius strip is a line bundle over the 1 sphere S1. Locally around every point in S1, it looks like U × R, but the total bundle is different from S1 × R (which is a cylinder instead). In mathematics, a vector bundle is a… …   Wikipedia

• Frame bundle — In mathematics, a frame bundle is a principal fiber bundle F(E) associated to any vector bundle E. The fiber of F(E) over a point x is the set of all ordered bases, or frames, for Ex. The general linear group acts naturally on F(E) via a change… …   Wikipedia

• Normal bundle — In differential geometry, a field of mathematics, a normal bundle is a particular kind of vector bundle, complementary to the tangent bundle, and coming from an embedding (or immersion). Contents 1 Definition 1.1 Riemannian manifold 1.2 …   Wikipedia

• Fiber bundle — In mathematics, in particular in topology, a fiber bundle (or fibre bundle) is a space which looks locally like a product space. It may have a different global topological structure in that the space as a whole may not be homeomorphic to a… …   Wikipedia

• Connection (vector bundle) — This article is about connections on vector bundles. See connection (mathematics) for other types of connections in mathematics. In mathematics, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; …   Wikipedia

• Cotangent bundle — In mathematics, especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold. It may be described also as the dual bundle to the tangent bundle.… …   Wikipedia