INVARIANT VOLUME FORMS AND FIRST INTEGRALS FOR GEODESICALLY EQUIVALENT FINSLER METRICS

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.

Automated summary

Two equivalent Finsler metrics determine a set of invariant volume forms, with their proportionality factors being geodesically invariant functions. These quantities are common for the entire projective class.