University of MaraghehSahand Communications in Mathematical Analysis2322-580721120240101Rigidity of Weak Einstein-Randers Spaces20722070799310.22130/scma.2023.1983170.1218ENBehnazLajmiriDepartment of Mathematics and Computer Science Amirkabir University of Technology (Tehran Polytechnic) 424 Hafez Ave. 15914 Tehran, Iran.0000-0000-0000-0000BehrozBidabadDepartment of Mathematics and Computer Science Amirkabir University of Technology (Tehran Polytechnic) 424 Hafez Ave. 15914 Tehran, Iran.0000-0003-3993-4268MehdiRafie-RadDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.0000-0000-0000-0000Journal Article20221219The 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 $k$.https://scma.maragheh.ac.ir/article_707993_ef0472721eb4c03f1c2ff833c5fe89d5.pdf