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arXiv · 2109.05915

Two-step homogeneous geodesics in some homogeneous Finsler manifolds

Masoumeh Hosseini·Hamid Reza Salimi Moghaddam
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Abstract

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.

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Masoumeh Hosseini, Hamid Reza Salimi Moghaddam. 2024-03-23. Two-step homogeneous geodesics in some homogeneous Finsler manifolds. https://doi.org/10.1007/s13226-025-00887-2

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