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Is there a construction in Riemannian geometry which relates the gradient flow of a function on a manifold with a certain metric with geodesics on another related manifold with its own metric?

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  • $\begingroup$ Well, geodesic flow is a skew-gradient flow for the riemannian metric. $\endgroup$ Aug 26, 2022 at 21:14
  • $\begingroup$ Could you elaborate on that a bit? Or give me a reference? $\endgroup$ Aug 28, 2022 at 15:24
  • $\begingroup$ geodesic flow is a skew-gradient flow for the riemannian metric on the tangent bundle with standard symplectic form. $\endgroup$ Aug 28, 2022 at 19:09

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