The prescribed Ricci curvature problem on 5-dimensional nilpotent Lie groups

Abstract

In this paper, using the Milnor-type theorem technique, we provide on each nilpotent five dimensional Lie group, some global existence result of a pair (g, c) consisting of a left-invariant Riemannian metric g and a positive constant c such that Ric(g) =cT, where Ric(g) is the Ricci curvature of g and T a given left-invariant symmetric (0, 2)-tensor field.