A deformation of quaternionic hyperbolic space

Abstract

We construct a continuous family of new homogeneous Einstein spaces with negative Ricci curvature, obtained by deforming from the quaternionic hyperbolic space of real dimension 12. We give an explicit description of this family, which is made up of Einstein solvmanifolds which share the same algebraic structure (eigenvalue type) as the rank one symmetric space H H 3 \mathbf {H}H^3 . This deformation includes a continuous family of new homogeneous Einstein spaces with negative sectional curvature.