In this paper we study the Riemannian geometry of simple Lie groups SO(3,R), SL(2,R) and SO(1,3), equipped with a left invariant Riemannian metric. We consider left invariant Randers metrics induced by these left invariant Riemannian metrics. Then, in each case, we obtain the S-curvature and show that although these Randers metrics are not of Berwald or Douglas type but in the case of SO(3,R) it is of almost isotropic S-curvature. Finally, we give the S-curvature of left invariant Randers metrics on four-dimensional Einstein Lie groups.
Abedi Karimi, H. (2021). S-Curvature of left invariant Randers metrics on some simple Lie groups. Journal of Finsler Geometry and its Applications, 2(2), 66-76. doi: 10.22098/jfga.2021.1369
MLA
Hossein Abedi Karimi. "S-Curvature of left invariant Randers metrics on some simple Lie groups". Journal of Finsler Geometry and its Applications, 2, 2, 2021, 66-76. doi: 10.22098/jfga.2021.1369
HARVARD
Abedi Karimi, H. (2021). 'S-Curvature of left invariant Randers metrics on some simple Lie groups', Journal of Finsler Geometry and its Applications, 2(2), pp. 66-76. doi: 10.22098/jfga.2021.1369
VANCOUVER
Abedi Karimi, H. S-Curvature of left invariant Randers metrics on some simple Lie groups. Journal of Finsler Geometry and its Applications, 2021; 2(2): 66-76. doi: 10.22098/jfga.2021.1369
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