Abstract.
Given two Riemannian metrics on a closed connected manifold \(M^n\), we construct self-adjoint differential operators \({\cal I}_0, {\cal I}_1,...,{\cal I}_{n-1}:C^2(M^n)\to C^0(M^n)\) such that if the metrics have the same geodesics then the operators commute with the Beltrami-Laplace operator of the first metric and pairwise commute. If the operators commute and if they are linearly independent, then the metrics have the same geodesics.
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Received: 11 February 2000; in final form: 20 August 2000/ Published online: 17 May 2001
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Matveev, V., Topalov, P. Quantum integrability of Beltrami-Laplace operator as geodesic equivalence. Math Z 238, 833–866 (2001). https://doi.org/10.1007/s002090100280
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DOI: https://doi.org/10.1007/s002090100280