Classification of Douglas (α, β)-metrics on five-dimensional nilpotent Lie groups

Abstract

In this paper, we classify all simply connected five-dimensional nilpotent Lie groups which admit (α,β)-metrics of Berwald and Douglas type defined by a left invariant Riemannian metric and a left invariant vector field. During this classification, we give the geodesic vectors, Levi-Civita connection, curvature tensor, sectional curvature and S-curvature. © 2020 World Scientific Publishing Company.