By a direct computation one can check that all the threedimensional
homogeneous spaces (pseudo-Riemannian manifolds with a threedimensional
group of isometries) have a constant scalar curvature. I will explain why
it is so, moreover, for any dimension. As a motivation we will mention
the structure of curvature tensor of a maximal symmetric space. We will
demonstrate that on homogeneous spaces also any scalar function of the
metric tensor and its derivatives is constant. For curiosity we will
present also Bianchi classification of threedimensional homogeneous spaces.