On some hypercomplex 4-dimensional Lie groups of constant scalar curvature

Abstract

In this paper we study sectional curvature of invariant hyper-Hermitian metrics on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. We give the Levi-Civita connections and explicit formulas for computing sectional curvatures of these metrics and show that all these spaces have constant scalar curvature. We also show that they are flat or they have only non-negative or non-positive sectional curvature.

Cited by in corpus (2)

• On the Randers metrics on two-step homogeneous nilmanifolds of dimension five
• Non-Berwaldian Randers metrics of Douglas type on four-dimensional hypercomplex Lie groups