Submanifolds of Noncompact Homogeneous Spaces with Special Curvature Properties

Abstract: 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 and submanifolds where the Ricci curvatures 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. We explore a new class of solvmanifolds defined by Kac-Moody algebras that are generalizations of symmetric spaces for which our crucial extra conditions hold. And furthermore, in current work in progress, we investigate other metric properties of these spaces.

This is joint work with Tracy Payne.

differential geometry

Audience: researchers in the topic

( video )

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Virtual seminar on geometry with symmetries

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