Randers Metrics of Berwald type on 4-dimensional hypercomplex Lie groups

Abstract

In the present paper we study Randers metics of Berwald type on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. On these spaces, the Randers metrics arising from invariant hyper-Hermitian metrics are considered. Then we give explicit formulas for computing flag curvature of these metrics. By this study we construct two 4-dimensional Berwald spaces, one of them has non-negative flag curvature and the other one has non-positive flag curvature.

References in corpus (4)

• Flag Curvature of Invariant Randers Metrics on Homogeneous Manifolds
• Almost hypercomplex pseudo-Hermitian manifolds and a 4-dimensional Lie group with such structure
• Flag curvature of invariant $(\alpha ,\beta )$-metrics of type $\frac{(\alpha +\beta {)}^2}{\alpha }$
• On the flag curvature of invariant Randers metrics

Cited by in corpus (1)

• The Relation Between Automorphism Group and Isometry Group of Randers Lie Groups