First integrals for Finsler metrics with vanishing $\chi$-curvature

Abstract

We prove that in a Finsler manifold with vanishing $\chi$-curvature (in particular with constant flag curvature) some non-Riemannian geometric structures are geodesically invariant and hence they induce a set of non-Riemannian first integrals. Two alternative expressions of these first integrals can be obtained either in terms of the mean Berwald curvature, or as functions of the mean Cartan torsion and the mean Landsberg curvature.

References in corpus (3)

• Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations
• A class of Finsler metrics admitting first integrals
• Invariant volume forms and first integrals for geodesically equivalent Finsler metrics