Left Invariant Randers Metrics of Berwald type on Tangent Lie Groups

Abstract

Let $G$ be a Lie group equipped with a left invariant Randers metric of Berward type $F$, with underlying left invariant Riemannian metric $g$. Suppose that $\tilde{F}$ and $\tilde{g}$ are lifted Randers and Riemannian metrics arising from $F$ and $g$ on the tangent Lie group $TG$ by vertical and complete lifts. In this article we study the relations between the flag curvature of the Randers manifold $(TG,\tilde{F})$ and the sectional curvature of the Riemannian manifold $(G,g)$ when $\tilde{F}$ is of Berwald type. Then we give all simply connected $3$-dimentional Lie groups such that their tangent bundles admit Randers metrics of Berwarld type and their geodesics vectors.

References in corpus (4)

• Homogeneous geodesics in homogeneous Finsler spaces
• Flag Curvature of Invariant Randers Metrics on Homogeneous Manifolds
• On the Randers metrics on two-step homogeneous nilmanifolds of dimension five
• On the left invariant Randers and Matsumoto metrics of Berwald type on 3-dimensional Lie groups

Cited by in corpus (2)

• On the Riemann-Finsler Geometry of Tangent Bundle of Lie Groups with Two-Dimensional Commutator Subgroup
• Left invariant lifted $(\alpha ,\beta )$-metrics of Douglas type on tangent Lie groups