The Alekseevskii Conjecture in 9 and 10 dimensions

Abstract

We show that noncompact homogeneous spaces not diffeomorphic to Euclidean space of dimension 9 or 10 admit no homogeneous Einstein metrics of negative Ricci curvature, with only three potential exceptions. The main ingredient in the proof is to show, via a cohomogeneity-one approach, that noncompact homogeneous spaces admitting an ideal isomorphic to ${\mathfrak{sl}}_2(\mathbb{R})$ admit no homogeneous Einstein metrics of negative Ricci curvature.

References in corpus (3)

• Strongly solvable spaces
• Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds
• Homogeneous Lorentzian manifolds of a semisimple group