Invariant volume forms and first integrals for geodesically equivalent Finsler metrics
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 0homogeneous 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.13374
 Bibcode:
 2021arXiv211113374B
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics;
 53C60;
 53B40;
 53D25;
 53A20
 EPrint:
 Proc. Amer. Math. Soc., 2022