Rigidity of Weak Einstein-Randers Spaces

Lajmiri, Behnaz; Bidabad, Behroz; Rafie-Rad, Mehdi

doi:10.22130/scma.2023.1983170.1218

Document Type : Research Paper

Authors

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.

https://doi.org/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

Main Subjects

Topology and Methods

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Sahand Communications in Mathematical Analysis

Rigidity of Weak Einstein-Randers Spaces

References

References

Volume 21, Issue 1
January 2024
Pages 207-220

Rigidity of Weak Einstein-Randers Spaces

References

References

Volume 21, Issue 1January 2024Pages 207-220

Volume 21, Issue 1
January 2024
Pages 207-220