论文标题
randers和$（α，β）$ equodesics，用于某种紧凑的同质流形
Randers and $(α,β)$ equigeodesics for some compact homogeneous manifolds
论文作者
论文摘要
$ g/h $上的平滑曲线如果是$ g/h $的所有$ g $ invariant riemannian指标，则称为Riemannian EquigeIgeIcic。通过$ g $ invariant Riemannian Metric取代了其他类别的$ g $ invariant指标，我们可以类似地定义Finsler Equigeodesic，Randers Equigeodesic，$（α，β）$ EquigeEdesic等。对于紧凑的同质歧管，我们证明了randers和$（α，β）$ equigeEdesics是等效的，并为它们找到标准。使用此标准，我们可以在许多紧凑的同质歧管上对公平学分类，这些谱系允许非Riemannian同质randers指标，包括四类均质球体。
A smooth curve on $G/H$ is called a Riemannian equigeodesic if it is a homogeneous geodesic for all $G$-invariant Riemannian metrics on $G/H$. With the $G$-invariant Riemannian metric replaced by other classes of $G$-invariant metrics, we can similarly define Finsler equigeodesic, Randers equigeodesic, $(α,β)$ equigeodesic, etc. In this paper, we study Randers and $(α,β)$ equigeodesics. For a compact homogeneous manifold, we prove Randers and $(α,β)$ equigeodesics are equivalent, and find a criterion for them. Using this criterion we can classify the equigeodesics on many compact homogeneous manifolds which permit non-Riemannian homogeneous Randers metrics, including four classes of homogeneous spheres.
