  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.
