
Journal of Lie Theory 29 (2019), No. 3, 619627 Copyright Heldermann Verlag 2019 On Flag Curvature and Homogeneous Geodesics of Left Invariant Randers Metrics on the SemiDirect 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 [Abstractpdf] 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, semidirect product. MSC: 53C60, 53C30 [ Fulltextpdf (109 KB)] for subscribers only. 