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

Year 2019, Volume: 12 Issue: 2, 218 - 222, 03.10.2019

Masumeh Nejadahmad Hamid Reza Salimi Moghaddam

https://doi.org/10.36890/iejg.628086

Abstract

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

Keywords

(α ¸ β)-metric, left invariant Finsler metric, left invariant Riemannian metric, curvature, nilpotent Lie group

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