Projective vector fields on special (α,β)-metrics

Document Type : Original Article

Author

Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran. E-mail: s.masoumi94@gmail.com

Abstract

In this paper, we study the projective vector fields on two special
(α,β)-metrics, namely Kropina and Matsumoto metrics. First, we consider
the Kropina metrics, and show that if a Kropina metric F = α2/β admits
a projective vector field, then this is a conformal vector field with respect to
Riemannian metric a or F has vanishing S-curvature. Then we study the
Matsumoto metric F = α2/(α−β) and prove that if the Matsumoto metric
F = α2/β admits a projective vector field, then this is a conformal vector field
with respect to Riemannian metric a or F has vanishing S-curvature.

Keywords

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Journal of Finsler Geometry and its Applications
Volume 1, Issue 2
December 2020
Pages 83-93

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