%0 Journal Article
%T Rigidity of Weak Einstein-Randers Spaces
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Lajmiri, Behnaz
%A Bidabad, Behroz
%A Rafie-Rad, Mehdi
%D 2024
%\ 01/01/2024
%V 21
%N 1
%P 207-220
%! Rigidity of Weak Einstein-Randers Spaces
%K Projective vector fields
%K Conformal vector fields
%K Randers metric
%K Weak Einstein
%K S-curvature
%K rigidity
%R 10.22130/scma.2023.1983170.1218
%X 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 $k$.
%U https://scma.maragheh.ac.ir/article_707993_ef0472721eb4c03f1c2ff833c5fe89d5.pdf