Shen, Zhongmin2022-09-072022-09-072021Shen, Z. (2021). On sprays with vanishing χ-curvature. International Journal of Mathematics, 32(10), 2150069. https://doi.org/10.1142/S0129167X215006950129-167X, 1793-6519https://hdl.handle.net/1805/29960Every 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.en-USPublisher Policyisotropic curvatureSpraysχ-curvatureS -curvatureArticle