Contents Online
Mathematical Research Letters
Volume 9 (2002)
Number 1
Commutative conservation laws for geodesic flows of metrics admitting projective symmetry
Pages: 65 – 72
DOI: https://dx.doi.org/10.4310/MRL.2002.v9.n1.a5
Author
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.
Published 1 January 2002