S-Curvature of left invariant Randers metrics on some simple Lie groups

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.