Commutative conservation laws for geodesic flows of metrics admitting projective symmetry

Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21971

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

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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.

Item Type:	Journal Article, refereed, original work
Communities & Collections:	07 Faculty of Science > Institute of Mathematics
DDC:	510 Mathematics
Language:	English
Date:	2002
Deposited On:	29 Nov 2010 17:27
Last Modified:	25 Nov 2012 08:51
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.
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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