Commutative Conservation Laws for Geodesic Flows of Metrics Admitting Projective Symmetry
نویسنده
چکیده
We prove that the geodesic flow of a pseudo-Riemannian metric g that admits a ”nontrivial” projective symmetry X is completely integrable. Nontriviality condition of the projective symmetry is expressed in the terms of the invariants of the pair forms g and LXg, where LX denotes the Lie derivative with respect to the vector field X. The theorem we propose can be considered as a ”commutative” analog of the Noether theorem. Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-21971 Originally published at: Topalov, P (2002). Commutative conservation laws for geodesic flows of metrics admitting projective symmetry. Mathematical Research Letters, 9(1):65-72. Mathematical Research Letters 9, 65–72 (2002) COMMUTATIVE CONSERVATION LAWS FOR GEODESIC FLOWS OF METRICS ADMITTING PROJECTIVE SYMMETRY
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