Invariant volume forms and first integrals for geodesically equivalent Finsler metrics
Differential Geometry
2022-08-02 v2 Mathematical Physics
math.MP
Abstract
Two geodesically (projectively) equivalent Finsler metrics determine a set of invariant volume forms on the projective sphere bundle. Their proportionality factors are geodesically invariant functions and hence they are first integrals. Being 0-homogeneous functions, the first integrals are common for the entire projective class. In Theorem 1.1 we provide a practical and easy way of computing these first integrals as the coefficients of a characteristic polynomial.
Cite
@article{arxiv.2111.13374,
title = {Invariant volume forms and first integrals for geodesically equivalent Finsler metrics},
author = {Ioan Bucataru},
journal= {arXiv preprint arXiv:2111.13374},
year = {2022}
}