On sprays with vanishing X-curvature
Differential Geometry
2020-08-19 v1
Abstract
Every Riemannian metric or Finsler metric on a manifold induces a spray via its geodesics. In this paper, we discuss several expressions for the X-curvature of a spray. We show that the sprays obtained by a projective deformation using the S-curvature always have vanishing X-curvature. Then we establish the Beltrami Theorem for sprays with X=0
Cite
@article{arxiv.2008.07732,
title = {On sprays with vanishing X-curvature},
author = {Zhongmin Shen},
journal= {arXiv preprint arXiv:2008.07732},
year = {2020}
}