On the Geometry of Some (α,β )-Metrics on the Nilpotent Groups H(p,r)

Abstract

In this paper we study the Riemann-Finsler geometry of the Lie groups H(p; r) which are ageneralization of the Heisenberg Lie groups. For a certain Riemannian metric h; i, the Levi-Civitaconnection and the sectional curvature are given. We classify all left invariant Randers metrics ofDouglas type induced by h; i, compute their flag curvatures and show that all of them are non-Berwaldian.