Geodesic
On Flag Curvature and Homogeneous Geodesics of Left Invariant Randers Metrics on the Semi-Direct Product a ⊕p r
Mahnaz Ebrahimi1; Dariush Latifi1
1Dept. of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran
Journal of Lie Theory, Volume 29 (2019) no. 3, pp. 619-627

See the original article notice from the Heldermann Verlag source

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.
Classification: 53C60, 53C30
Keywords: Invariant metric, Randers metric, flag curvature, homogeneous geodesics, semi-direct product

Mahnaz Ebrahimi  1 ; Dariush Latifi  1

1 Dept. of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran 
Mahnaz Ebrahimi; Dariush Latifi. On Flag Curvature and Homogeneous Geodesics of Left Invariant Randers Metrics on the Semi-Direct Product a ⊕p r. Journal of Lie Theory, Volume 29 (2019) no. 3, pp. 619-627. http://geodesic.mathdoc.fr/item/JOLT_2019_29_3_a2/
@article{JOLT_2019_29_3_a2,
     author = {Mahnaz Ebrahimi and Dariush Latifi},
     title = {On {Flag} {Curvature} and {Homogeneous} {Geodesics} of {Left} {Invariant} {Randers} {Metrics} on the {Semi-Direct} {Product} a \ensuremath{\oplus}\protect\textsubscript{p} r},
     journal = {Journal of Lie Theory},
     pages = {619--627},
     year = {2019},
     volume = {29},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2019_29_3_a2/}
}
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