Left invariant Randers metrics on the 3-dimensional Heisenberg group

Abstract

Abstract. In the present paper we give a complete description of the ChernRund connection defined by a left invariant Randers metric on the 3 dimensional Heisenberg group.

On the Finsler geometry of the Heisenberg group $H_{2n+1}$ and its extension

“…On the other hand Finsler metrics which are a generalization of Riemannian metrics on these spaces have been studied in the recent years. For example, recently left-invariant Randers metrics on three and five dimensional Heisenberg groups have been investigated in [16,17]. Also in [20] we investigated left-invariant Randers metrics of Douglas type on two-step nilpotent Lie groups of dimension five and in [22] and [12] this study is extended to a (2n + 1)-dimensional Heisenberg group with a special left-invariant Randers metric.…”