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, Tome 29 (2019) no. 3, pp. 619-627

Voir la notice de l'article provenant de la source Heldermann Verlag

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
Mots-clés : 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, Tome 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/}
}
TY  - JOUR
AU  - Mahnaz Ebrahimi
AU  - Dariush Latifi
TI  - On Flag Curvature and Homogeneous Geodesics of Left Invariant Randers Metrics on the Semi-Direct Product a ⊕p r
JO  - Journal of Lie Theory
PY  - 2019
SP  - 619
EP  - 627
VL  - 29
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JOLT_2019_29_3_a2/
ID  - JOLT_2019_29_3_a2
ER  - 
%0 Journal Article
%A Mahnaz Ebrahimi
%A Dariush Latifi
%T On Flag Curvature and Homogeneous Geodesics of Left Invariant Randers Metrics on the Semi-Direct Product a ⊕p r
%J Journal of Lie Theory
%D 2019
%P 619-627
%V 29
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2019_29_3_a2/
%F JOLT_2019_29_3_a2