University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002220211201S-Curvature of left invariant Randers metrics on some simple Lie groups6676136910.22098/jfga.2021.1369ENHossein Abedi KarimiDepartment of Mathematics,
Isfahan University of Technology, Isfahan, 84156-83111-Iran. hossein.abedikarimi@gmail.comJournal Article20210821In 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.https://jfga.uma.ac.ir/article_1369_5baec535882f158e3d98872493c5cacf.pdf