# 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
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• 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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