since M is a submanifold of N, near any point p of M, there is a chart of N so that M is defined by . TN can be parametrized by where any tangent vector . And TM can be parametrized by , that is,
I'm trying to do this problem
"Prove that if is a submanifold of a manifold , then is a submanifold of "
what I've thought so far is following:
Let be charts of . Since is a submanifold of , can be covered by a collection of with the property ( is the dimension of ). Let , I think I have to prove that can be covered by the collection of with the property
Could anyone give me suggestions or comments?