Quantum integrability of Beltrami-Laplace operator as geodesic equivalence |
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| Authors: | Vladimir S. Matveev Peter J. Topalov |
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| Affiliation: | Mathematisches Institut, Universit?t Freiburg, Eckerstr. 1, 79104 Freiburg i. Br., Germany (e-mail: matveev@arcade.mathematik.uni-freiburg.de), DE
Department of Math. Differential Equation, Institute of Mathematics and Informatics, BAS, Sofia 1113, Bulgaria (e-mail: topalov@math.bas.bg), BG
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| Abstract: | Given two Riemannian metrics on a closed connected manifold , we construct self-adjoint differential operators 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. Received: 11 February 2000; in final form: 20 August 2000/ Published online: 17 May 2001 |
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