Conformal vector fields on compact connected homogeneous Finsler manifolds
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914666281697280 |
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| author | Xu, Ming |
| author_facet | Xu, Ming |
| contents | Let $(M,F)$ be a compact connected homogeneous non-Riemannian Finsler manifold with $\dim M>1$. We prove that any conformal vector field on $(M,F)$ is a Killing vector field. Further more, we prove that $ρF$ is a homogeneous Finsler metric on $M$ if and only if $ρ$ is a positive constant function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02406 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal vector fields on compact connected homogeneous Finsler manifolds Xu, Ming Differential Geometry Let $(M,F)$ be a compact connected homogeneous non-Riemannian Finsler manifold with $\dim M>1$. We prove that any conformal vector field on $(M,F)$ is a Killing vector field. Further more, we prove that $ρF$ is a homogeneous Finsler metric on $M$ if and only if $ρ$ is a positive constant function. |
| title | Conformal vector fields on compact connected homogeneous Finsler manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2402.02406 |