Isotropic Berwald metrics are as a generalization of Berwald metrics. Shen proved that every Berwald metric is of vanishing S-curvature. In this paper, we generalize this fact and prove that every isotropic Berwald metric is of isotropic S-curvature. Let F = α + β be a Randers metric of isotropic Berwald curvature. Then it corresponds to a conformal vector field through navigation representation.
Abstract. The collection of all projective vector fields on a Finsler space (M, F ) is a finitedimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra denoted by p(M, F ) and is the Lie algebra of the projective group P (M, F ). The projective algebra p(M, F = α + β) of a Randers space is characterized as a certain Lie subalgebra of the projective algebra p(M, α). Certain subgroups of the projective group P (M, F ) and their invariants are studied. The projective algebra of Randers metrics of constant flag curvature is studied and it is proved that the dimension of the projective algebra of Randers metrics constant flag curvature on a compact n-manifold either equals n(n + 2) or at most is n(n+1) 2 .
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