Let's suppose we have $N$ a compact Riemann manifold and a smooth function f on N. Prove that $\nabla f= 0$ at 2 or more points.
I am not very sure that this question is correct because I don't see how the fact that N is Riemannian fits.
Let's suppose we have $N$ a compact Riemann manifold and a smooth function f on N. Prove that $\nabla f= 0$ at 2 or more points.
I am not very sure that this question is correct because I don't see how the fact that N is Riemannian fits.