University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201Projective vector fields on special (α,β)-metrics8393124210.22098/jfga.2020.1242ENSaeedeh MasoumiDepartment of Mathematics, Faculty of Science,
Urmia University, Urmia, Iran.
E-mail: s.masoumi94@gmail.comJournal Article20210725In this paper, we study the projective vector fields on two special<br />(α,β)-metrics, namely Kropina and Matsumoto metrics. First, we consider<br />the Kropina metrics, and show that if a Kropina metric F = α<sup>2</sup>/β admits<br />a projective vector field, then this is a conformal vector field with respect to<br />Riemannian metric a or F has vanishing S-curvature. Then we study the<br />Matsumoto metric F = α<sup>2</sup>/(α−β) and prove that if the Matsumoto metric<br />F = α<sup>2</sup>/β admits a projective vector field, then this is a conformal vector field<br />with respect to Riemannian metric a or F has vanishing <strong>S</strong>-curvature.https://jfga.uma.ac.ir/article_1242_acc3899280480efa9b03c9e4c2609266.pdf