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. 
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2 Citations

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FIRST INTEGRALS FOR FINSLER METRICS WITH VANISHING χ-CURVATURE
. 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
. 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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