On sprays with vanishing X-curvature

Zhongmin Shen

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arXiv · 2008.07732

On sprays with vanishing X-curvature

Zhongmin Shen

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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

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Zhongmin Shen. 2020-08-18. On sprays with vanishing X-curvature. https://arxiv.org/abs/2008.07732

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