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arXiv · 2111.13374

Invariant volume forms and first integrals for geodesically equivalent Finsler metrics

Ioan Bucataru
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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.

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Ioan Bucataru. 2021-11-26. Invariant volume forms and first integrals for geodesically equivalent Finsler metrics. https://doi.org/10.1090/proc%2F15961

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