Abstract
In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold.
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Tian, Hj. Projective vector fields on Finsler manifolds. Appl. Math. J. Chin. Univ. 29, 217–229 (2014). https://doi.org/10.1007/s11766-014-3130-5
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DOI: https://doi.org/10.1007/s11766-014-3130-5