Hi, I have geometry questions.

I need your help.

Thank you so much.

Problem 6: The product manifold N x M admits two projection maps, which we denote TN : N XM - N TM : N XM - M. Prove that the sum of the induced maps of tangent bundles TRNOTTM : T(N X M) - TN x TM is a diffeomorphism. Problem 7 Argue that 2 x 2 matrices of rank 1 is a manifold. Denote this space by M1 (2, 2), i.e. we consider M1 (2, 2) to be a subspace of M2,2 (R) = 4