Invariant Einstein Kropina metrics on Lie groups and homogeneous spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2018
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911962247462912 |
|---|---|
| author | Hosseini, Masoumeh Moghaddam, Hamid Reza Salimi |
| author_facet | Hosseini, Masoumeh Moghaddam, Hamid Reza Salimi |
| contents | In this article, we study Einstein Kropina metrics on Lie groups and homogeneous spaces. We give a method to construct Einstein Kropina metrics on Lie groups. As an example of this method, a family of non-Riemannian Einstein Kropina metrics on the special orthogonal group $SO(n)$ is given. Then, we classify all left invariant Einstein Kropina metrics on simply connected $3$-dimensional real Lie groups. We provide a procedure to build Einstein Kropina metrics on homogeneous spaces. Using this technique, we study invariant Einstein Kropina metrics on spheres. Finally, we show that projective spaces do not admit any homogeneous non-Riemannian Einstein Kropina metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1807_10666 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Invariant Einstein Kropina metrics on Lie groups and homogeneous spaces Hosseini, Masoumeh Moghaddam, Hamid Reza Salimi Differential Geometry 53C30, 53C60, 53C25, 22E60 In this article, we study Einstein Kropina metrics on Lie groups and homogeneous spaces. We give a method to construct Einstein Kropina metrics on Lie groups. As an example of this method, a family of non-Riemannian Einstein Kropina metrics on the special orthogonal group $SO(n)$ is given. Then, we classify all left invariant Einstein Kropina metrics on simply connected $3$-dimensional real Lie groups. We provide a procedure to build Einstein Kropina metrics on homogeneous spaces. Using this technique, we study invariant Einstein Kropina metrics on spheres. Finally, we show that projective spaces do not admit any homogeneous non-Riemannian Einstein Kropina metrics. |
| title | Invariant Einstein Kropina metrics on Lie groups and homogeneous spaces |
| topic | Differential Geometry 53C30, 53C60, 53C25, 22E60 |
| url | https://arxiv.org/abs/1807.10666 |