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Let a Riemannian manifold $M$, it is possible to write all Riemannian metrics $g$ of manifold $M$ is polar coordinates, if it is possible what guarantees this? To finish, what is the expression general for this metric?

hardmath
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Cézar Bezerra
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    I am not understand you well. If you mean the global polar coordinates, there is not . But locally, just by Exp , the polar coordinate in $T_xM$ can be pushed to location of $x$. – Enhao Lan Dec 20 '16 at 12:28

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