Invariant volume forms and first integrals for geodesically equivalent Finsler metrics

Bucataru, Ioan

doi:10.1090/proc/15961

Invariant volume forms and first integrals for geodesically equivalent Finsler metrics
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by Ioan Bucataru PDF

Proc. Amer. Math. Soc. 150 (2022), 4475-4486 Request permission

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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