Mathematical Research Letters

Volume 9, Issue 1, January 2002 pp. 65-72.

Commutative conservation laws for geodesic flows of metrics admitting projective symmetry

Authors: Peter Topalov
Author institution: Universität Zürich

Summary: 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.

Contents Full-Text PDF