Schouten-like Metrics on Five-Dimensional Nilpotent Lie Groups

The prescribed Ricci curvature problem consists of finding a Riemannian metric $g$ to satisfy the equation $Ric(g) = T$, for some fixed symmetric $(0,2)$-tensor field $T$ on a differential manifold $M$. In this paper, we define Schouten-like metric as a particular solution of a prescribed Ricci curvature problem, and we classify them on five-dimensional nilpotent Lie groups by establishing a link with algebraic Schouten solitons.