Properties of non-Berwaldian Randers metric of Douglas type on 4-dimensional hypercomplex Lie groups

Abstract

In this paper, we first obtain the non-Berwaldian Randers metrics of Douglas type on 4-dimensional hypercomplex simply connected Lie groups. Then we give the S-curvature formulas for the non-Berwaldian Randers metric of Douglas type on these spaces. We also give some geometric properties and results on these spaces. We show that there is not any non-Berwaldian Randers metric of Douglas type on these Lie groups which have vanishing S-curvature and these spaces are never naturally reductive. Finally, we determine the geodesic vectors of Randers metrics on 4-dimensional hypercomplex simply connected Lie groups.