Browsing by Subject "Sprays"

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    On sprays with vanishing χ-curvature
    (World Scientific, 2021) Shen, Zhongmin; Mathematical Sciences, School of Science
    Every Riemannian metric or Finsler metric on a manifold induces a spray via its geodesics. In this paper, we discuss several expressions for the χ-curvature of a spray. We show that the sprays obtained by a projective deformation using the S-curvature always have vanishing χ-curvature. Then we establish the Beltrami Theorem for sprays with χ=0.