Let $\xi$ be a vector field on manifold $M^n$ which is a gradient-like vector field for a some Morse function $f$. Prove that there exists a Riemannian metric on $M$ such that $\xi$ is a gradient vector field for $M$.
2026-03-26 07:43:11.1774510991
Making a gradient-like vector field a gradient vector field via choosing a Riemannian metric.
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