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Книга: Tangent Bundle: Mathematics, Differentiable Manifold, Disjoint Union, Tangent Space, Projection (mathematics), Vector Bundle, Fiber Bundle, Dual Bundle, Disjoint Union (topology), Frame Bundle

Товар № 10199001
Вес: 0.170 кг.
Год издания: 2010
Страниц: 80 Переплет: Мягкая обложка
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High Quality Content by WIKIPEDIA articles! The tangent bundle to a manifold is the prototypical example of a vector bundle (a fiber bundle whose fibers are vector spaces). A section of TM is a vector field on M, and the dual bundle to TM is the cotangent bundle, which is the disjoint union of the cotangent spaces of M. By definition, a manifold M is parallelizable if and only if the tangent bundle is trivial. By definition, a manifold M is framed if and only if the tangent bundle TM is stably trivial, meaning that for some trivial bundle E the Whitney sum TM oplus E is trivial.

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