# Invariant volume forms and first integrals for geodesically equivalent Finsler metrics

@inproceedings{Bucataru2022InvariantVF, title={Invariant volume forms and first integrals for geodesically equivalent Finsler metrics}, author={Ioan Bucataru}, year={2022} }

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.

## 2 Citations

FIRST INTEGRALS FOR FINSLER METRICS WITH VANISHING χ-CURVATURE

- Mathematics
- 2022

. We prove that in a Finsler manifold with vanishing χ -curvature (in particular with constant ﬂag curvature) some non-Riemannian geometric structures are geodesically invariant and hence they induce…

First integrals for Finsler metrics with vanishing $\chi$-curvature

- Mathematics
- 2022

. We prove that in a Finsler manifold with vanishing χ -curvature (in particular with constant ﬂag curvature) some non-Riemannian geometric structures are geodesically invariant and hence they induce…

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