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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.

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    Awesome related fact (due to Reeb): If you can cook up such an $f$ with $\nabla f = 0$ at exactly $2$ points, $N$ is homeomorphic to a sphere!2012-12-22

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