Noncompact homogeneous Einstein 5-manifolds (Q2572553)

Let \(M^n\) be a simply connected \(n\)-dimensional homogeneous Einstein manifold. It is well known that \(M\) is a space of constant curvature if \(n \in \{2,3\}\). For \(n=4\) \textit{G. R. Jensen} proved in [J. Differ. Geom. 3, 309--349 (1969; Zbl 0194.53203)] that \(M\) is a symmetric space. For \(n=5\) and compact \(M\) a classification was obtained by \textit{D. Alekseevsky, I. Dotti} and \textit{C. Ferraris} in [Pac. J. Math. 175, No. 1, 1--12 (1996; Zbl 0865.53041)]. The main result of the present paper is the classification for \(n=5\) and noncompact \(M\) with negative Ricci curvature. Any such Einstein manifold is a solvmanifold corresponding to one of five types of metric Lie algebras. All of these Einstein solvmanifolds are known from earlier work by \textit{D. Alekseevsky} in [Math. USSR, Sb. 25(1975), 87--109 (1976; Zbl 0325.53043) translation from Mat. Sb., N. Ser. 96(138), 93--117 (1975; Zbl 0309.53037)].