The Relation Between Automorphism Group and Isometry Group of Left Invariant $ (α,β)$-metrics
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Acceso en línea: | |
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| _version_ | 1866917728047071232 |
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| author | Nejadahmad, Masumeh Moghaddam, Hamid Reza Salimi |
| author_facet | Nejadahmad, Masumeh Moghaddam, Hamid Reza Salimi |
| contents | This work generalizes the results of an earlier paper by the second author, from Randers metrics to $(α,β)$-metrics. Let $F$ be an $(α,β)$-metric which is defined by a left invariant vector field and a left invariant Riemannian metric on a simply connected real Lie group $G$. We consider the automorphism and isometry groups of the Finsler manifold $(G,F)$ and their intersection. We prove that for an arbitrary left invariant vector field $X$ and any compact subgroup $K$ of automorphisms which $X$ is invariant under them, there exists an $(α,β)$-metric such that $K$ is a subgroup of its isometry group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_02528 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The Relation Between Automorphism Group and Isometry Group of Left Invariant $ (α,β)$-metrics Nejadahmad, Masumeh Moghaddam, Hamid Reza Salimi Differential Geometry 53C60, 58B20, 20F28 This work generalizes the results of an earlier paper by the second author, from Randers metrics to $(α,β)$-metrics. Let $F$ be an $(α,β)$-metric which is defined by a left invariant vector field and a left invariant Riemannian metric on a simply connected real Lie group $G$. We consider the automorphism and isometry groups of the Finsler manifold $(G,F)$ and their intersection. We prove that for an arbitrary left invariant vector field $X$ and any compact subgroup $K$ of automorphisms which $X$ is invariant under them, there exists an $(α,β)$-metric such that $K$ is a subgroup of its isometry group. |
| title | The Relation Between Automorphism Group and Isometry Group of Left Invariant $ (α,β)$-metrics |
| topic | Differential Geometry 53C60, 58B20, 20F28 |
| url | https://arxiv.org/abs/1911.02528 |