Left invariant Randers metrics of Berwald type on tangent Lie groups
Abstract
Let G be a Lie group equipped with a left invariant Randers metric of Berward type F, with underlying left invariant Riemannian metric g. Suppose that F∼ and g∼ are lifted Randers and Riemannian metrics arising from F and g on the tangent Lie group TG by vertical and complete lifts. In this paper, we study the relations between the flag curvature of the Randers manifold (TG,F∼) and the sectional curvature of the Riemannian manifold (G,g) when F∼ is of Berwald type. Then we give all simply connected three-dimensional Lie groups such that their tangent bundles admit Randers metrics of Berwarld type and their geodesics vectors.
- Publication:
-
International Journal of Geometric Methods in Modern Physics
- Pub Date:
- 2018
- DOI:
- 10.1142/S0219887818500159
- arXiv:
- arXiv:1610.01474
- Bibcode:
- 2018IJGMM..1550015A
- Keywords:
-
- Left invariant Finsler metric;
- Randers metric;
- complete and vertical lifts;
- flag curvature;
- Mathematics - Differential Geometry;
- Mathematical Physics
- E-Print:
- International Journal of Geometric Methods in Modern PhysicsVol. 15, No. 01, 1850015 (2018)