English

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

Differential Geometry 2022-10-28 v1 Mathematical Physics math.MP

Abstract

We prove that in a Finsler manifold with vanishing χ\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.

Keywords

Cite

@article{arxiv.2204.05678,
  title  = {First integrals for Finsler metrics with vanishing $\chi$-curvature},
  author = {Ioan Bucataru and Oana Constantinescu and Georgeta Cretu},
  journal= {arXiv preprint arXiv:2204.05678},
  year   = {2022}
}