The push forward of vectors on manifolds

Описание: The pushforward of a vector is a fundamental concept in differential geometry, particularly when dealing with differentiable maps between manifolds. It provides a way to map vectors from one tangent space on a manifold to another tangent space on a different manifold, respecting the smooth structure of the manifolds and the differentiable map between them. In the case of a coordinate change the two manifolds are the same just equipped with different coordinate systems.