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# Mathematical Research Letters

## Volume 9 (2002)

### Number 1

### Commutative conservation laws for geodesic flows of metrics admitting projective symmetry

Pages: 65 – 72

DOI: http://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.