Two-step homogeneous geodesics in some homogeneous Finsler manifolds

Fuente: arXiv
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Main Authors: Hosseini, Masoumeh, Moghaddam, Hamid Reza Salimi
Format: Preprint
Published: 2021
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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