@article {
author = {Lajmiri, Behnaz and Bidabad, Behroz and Rafie-Rad, Mehdi},
title = {Rigidity of Weak Einstein-Randers Spaces},
journal = {Sahand Communications in Mathematical Analysis},
volume = {21},
number = {1},
pages = {207-220},
year = {2024},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2023.1983170.1218},
abstract = {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 $k$.},
keywords = {Projective vector fields,Conformal vector fields,Randers metric,Weak Einstein,S-curvature,rigidity},
url = {https://scma.maragheh.ac.ir/article_707993.html},
eprint = {https://scma.maragheh.ac.ir/article_707993_ef0472721eb4c03f1c2ff833c5fe89d5.pdf}
}