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

Document Type : Original Article

Author

Department of Mathematics, Isfahan University of Technology, Isfahan, 84156-83111-Iran. hossein.abedikarimi@gmail.com

Abstract

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.

Keywords

References

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Journal of Finsler Geometry and its Applications
Volume 2, Issue 2
December 2021
Pages 66-76

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