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INVARIANT VOLUME FORMS AND FIRST INTEGRALS FOR GEODESICALLY EQUIVALENT FINSLER METRICS

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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
卷 150, 期 10, 页码 4475-4486

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AMER MATHEMATICAL SOC
DOI: 10.1090/proc/15961

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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.
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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