First integrals for Finsler metrics with vanishing χ-curvature

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.

Automated summary

In this study, we prove that certain non-Riemannian geometric structures in a Finsler manifold with vanishing chi-curvature, particularly with constant flag curvature, are geodesically invariant and as a result, they give rise to a set of non-Riemannian first integrals. These first integrals can be expressed either in terms of the mean Berwald curvature or as functions of the mean Cartan torsion and the mean Landsberg curvature.