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First integrals for Finsler metrics with vanishing χ-curvature

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY (2022)

INVARIANT VOLUME FORMS AND FIRST INTEGRALS FOR GEODESICALLY EQUIVALENT FINSLER METRICS

Ioan Bucataru

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.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2022)

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Article Mathematics

On sprays with vanishing χ-curvature

Zhongmin Shen

Summary: This paper discusses the chi-curvature of sprays induced by Riemannian or Finsler metrics on a manifold, showing that sprays obtained through projective deformation using S-curvature always have vanishing chi-curvature. The Beltrami Theorem for sprays with chi = 0 is also established in this study.

INTERNATIONAL JOURNAL OF MATHEMATICS (2021)

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Article Mathematics, Applied

A class of Finsler metrics admitting first integrals

Ioan Bucataru et al.

Summary: In this study, two non-Riemannian curvature tensors, chi-curvature and mean Berwald curvature, are used to characterize a class of Finsler metrics with first integrals. This class also encompasses Finsler metrics of constant flag curvature.

JOURNAL OF GEOMETRY AND PHYSICS (2021)

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Article Mathematics