Suppose we have a Hamiltonian dynamics on a phase space, whose base space is also a Riemannian manifold. I was wondering if the Hamiltonian trajectories are whether geodesics or only locally geodesics on the cotangent bundle? Thanks!
2026-03-24 23:44:25.1774395865
Are Hamiltonian trajectories geodesics on the cotangent bundle?
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A short answer is yes, but we need some more restriction on the Hamiltonian we are choosing. See: https://en.wikipedia.org/wiki/Geodesics_as_Hamiltonian_flows .