The Ricci curvature form of a submanifold is not, in general, the restriction of the Ricci curvature of the ambient space. Therefore, classes of manifolds on which the Ricci curvatures of some submanifolds are aligned are very special. Indeed, Tamaru exploited this idea in the setting of noncompact symmetric spaces to construct new examples of Einstein solvmanifolds via special subalgebras. We characterize the largest category in which Tamaru's construction can be extended, identifying two crucial algebraic/metric conditions. On Kac-Moody solvmanifolds, our crucial extra conditions hold. In current work in progress, we investigate other geometric properties of these spaces.

This is joint work with Tracy Payne (Idaho State University).