Inhomogeneous isoparametric hypersurfaces in symmetric spaces of noncompact type

Abstract: A hypersurface of a Riemannian manifold is called isoparametric if its nearby parallel hypersurfaces have constant mean curvature. Homogeneous hypersurfaces, that is, codimension one orbits of isometric actions, constitute a fundamental class of examples. The problem of determining which spaces with a large isometry group admit inhomogeneous isoparametric hypersurfaces has a long history that traces back to Élie Cartan.

In this talk, I will report on a joint work with Víctor Sanmartín-López where we construct the first examples of inhomogeneous isoparametric hypersurfaces in every symmetric space of noncompact type and rank at least three.

differential geometry

Audience: researchers in the topic

Differential Geometry Seminar Torino

Series comments: This is a hybrid seminar organized by the Differential Geometry groups of Università and Politecnico di Torino.

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