A tangent bundle is the collection of all of the tangent spaces for all points on a manifold, structured in a way that it forms a new manifold itself....
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Differentiable manifold (section Tangent bundle)
2n. The tangent bundle is where tangent vectors lie, and is itself a differentiable manifold. The Lagrangian is a function on the tangent bundle. One can...
67 KB (9,495 words) - 02:22, 11 July 2024
to the manifold at that point. Tangent bundles are not, in general, trivial bundles. For example, the tangent bundle of the sphere is non-trivial by...
31 KB (4,089 words) - 16:41, 9 April 2024
frame bundle of a smooth manifold is the one associated with its tangent bundle. For this reason it is sometimes called the tangent frame bundle. Let E...
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Vector field (redirect from Tangent bundle section)
setting, a vector field gives a tangent vector at each point of the manifold (that is, a section of the tangent bundle to the manifold). Vector fields...
28 KB (4,072 words) - 02:53, 8 September 2024
the unit tangent bundle of a Riemannian manifold (M, g), denoted by T1M, UT(M) or simply UTM, is the unit sphere bundle for the tangent bundle T(M). It...
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vector bundle in question is the tangent bundle T M {\displaystyle TM} , the unit sphere bundle is known as the unit tangent bundle. A sphere bundle is partially...
29 KB (4,085 words) - 13:01, 12 September 2024
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...
8 KB (1,437 words) - 16:33, 28 June 2022
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)...
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point in the manifold. It may be described also as the dual bundle to the tangent bundle. This may be generalized to categories with more structure than...
9 KB (1,472 words) - 13:16, 8 January 2024