Document Type : Research Paper


1 Department of Mathematics and Computer Science Amirkabir University of Technology (Tehran Polytechnic) 424 Hafez Ave. 15914 Tehran, Iran.

2 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.


The Randers metrics are popular metrics similar to the Riemannian metrics, frequently used in physical and geometric studies. The weak Einstein-Finsler metrics are a natural generalization of the Einstein-Finsler metrics. Our proof shows that if $(M,F)$ is a simply-connected and compact Randers manifold and $F$ is a weak Einstein-Douglas metric, then every special projective vector field is Killing on $(M,F)$. Furthermore, we demonstrate that if a connected and compact manifold $M$ of dimension $n \geq 3$ admits a weak Einstein-Randers metric with Zermelo navigation data $(h,W)$, then either the $S$-curvature of $(M,F)$ vanishes, or $(M,h)$ is isometric to a Euclidean sphere ${\mathbb{S}^n}(\sqrt{k})$, with a radius of $1/\sqrt{k}$, for some positive integer $k$.


Main Subjects

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