Journal of Lie Theory 29 (2019), No. 3, 619--627
Copyright Heldermann Verlag 2019
On Flag Curvature and Homogeneous Geodesics of Left Invariant Randers Metrics on the Semi-Direct Product a ⊕p r
Mahnaz Ebrahimi
Dept. of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran
m.ebrahimi@uma.ac.ir
Dariush Latifi
Dept. of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran
latifi@uma.ac.ir
[Abstract-pdf]
We study flag curvature and homogeneous geodesics of left invariant Randers metrics on the Lie group with Lie algebra $\mathfrak{a}\oplus_{\mathfrak{p}}\mathfrak{r}$, where $\mathfrak{a}$ and $\mathfrak{r}$ are abelian Lie algebra of dimension $n$ and $1$, respectively. We give their flag curvature formulas explicitly. We show that there is an $(n+1)-$dimensional Lie group with left invariant Randers metric which admits exactly one homogeneous geodesic.
Keywords: Invariant metric, Randers metric, flag curvature, homogeneous geodesics, semi-direct product.
MSC: 53C60, 53C30
[ Fulltext-pdf (109 KB)] for subscribers only.