Two-step homogeneous geodesics in some homogeneous Finsler manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866917445759926272 |
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| author | Hosseini, Masoumeh Moghaddam, Hamid Reza Salimi |
| author_facet | Hosseini, Masoumeh Moghaddam, Hamid Reza Salimi |
| contents | A natural extension of a homogeneous geodesic in homogeneous Riemannian spaces $G/H$, known as a two-step homogeneous geodesic, can be expressed of the form $γ(t)=π(\exp(tx)\exp(ty))$, where $x$ and $y$ are elements of the Lie algebra of $G$. This paper aims to expand this concept to homogeneous Finsler spaces. We provide certain sufficient conditions for $(α,β)$ spaces and decomposable cubic spaces to possess a one-parameter family of invariant Finsler metrics that can be classified as two-step Finsler geodesic orbit spaces. Additionally, we present some illustrative examples of these spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_05915 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Two-step homogeneous geodesics in some homogeneous Finsler manifolds Hosseini, Masoumeh Moghaddam, Hamid Reza Salimi Differential Geometry 53C30, 53C60, 53C25, 22E60 A natural extension of a homogeneous geodesic in homogeneous Riemannian spaces $G/H$, known as a two-step homogeneous geodesic, can be expressed of the form $γ(t)=π(\exp(tx)\exp(ty))$, where $x$ and $y$ are elements of the Lie algebra of $G$. This paper aims to expand this concept to homogeneous Finsler spaces. We provide certain sufficient conditions for $(α,β)$ spaces and decomposable cubic spaces to possess a one-parameter family of invariant Finsler metrics that can be classified as two-step Finsler geodesic orbit spaces. Additionally, we present some illustrative examples of these spaces. |
| title | Two-step homogeneous geodesics in some homogeneous Finsler manifolds |
| topic | Differential Geometry 53C30, 53C60, 53C25, 22E60 |
| url | https://arxiv.org/abs/2109.05915 |