13. Consider S-1 as a submanifold of S* via the usual embedding mapping (x1,...,x) (x1,...,xk, 0). Show that at p = S*-1 the orthogonal -> complement to T,(S-1) in T,(S) is spanned by the vector (0, . . ., 0, 1). Prove that N(S-1; S*) is diffeomorphic to S*-1 x R.