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Commutative conservation laws for geodesic flows of metrics admitting projective symmetry


Topalov, P (2002). Commutative conservation laws for geodesic flows of metrics admitting projective symmetry. Mathematical Research Letters, 9(1):65-72.

Abstract

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 $L_Xg$, where $L_X$ 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.

Abstract

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 $L_Xg$, where $L_X$ 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2002
Deposited On:29 Nov 2010 16:27
Last Modified:19 Feb 2018 21:36
Publisher:International Press
ISSN:1073-2780
Additional Information:First published in [Mathematical Research Letters] in [9 (2002), no. 1], published by International Press. Copyright © 2002 Mathematical Research Letters. All rights reserved.
OA Status:Green
Official URL:http://www.mrlonline.org/mrl/2002-009-001/2002-009-001-005.html
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1892314
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A05375219

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