Quantum integrability of Beltrami-Laplace operator as geodesic equivalence (Q5956860)

Two Riemannian metrics on the same manifold are called geodesically equivalent if they have the same geodesics considered as unparametrized curves. In this paper, given two Riemannian metrics on a closed connected manifold, the authors construct \(n\) self-adjoint differential operators such that if the metrics have the same geodesics then the operators commute pairwise and with the Beltrami-Laplace operator of the first metric. If the operators commute and if they are linearly independent, then the metrics have the same geodesics.