The prescribed Ricci curvature problem on five-dimensional nilpotent Lie groups

In this paper, using the Milnor-type theorem technique for each left-invariant symmetric [Formula: see text]-tensor field [Formula: see text] on a five-dimensional nilpotent Lie group, we determine whether it is possible or not to find a left-invariant Riemannian metric [Formula: see text] and a constant [Formula: see text] so that [Formula: see text], where [Formula: see text] is the Ricci curvature of [Formula: see text].