Cohomogeneity one actions on symmetric spaces of noncompact type

Abstract: The classification of cohomogeneity one actions (up to orbit equivalence) on real hyperbolic spaces is known since Cartan's investigation of isoparametric hypersurfaces in the late 1930s. The analogous classification for the other rank one symmetric spaces of noncompact type was only concluded very recently. For higher rank, several partial results have been obtained by Berndt and Tamaru, but complete classifications are only known for some rank two irreducible spaces.

In this talk I will report on a joint work in progress with J. Carlos Díaz-Ramos and Tomás Otero-Casal where we provide a new structural result for cohomogeneity one actions on symmetric spaces of noncompact type and arbitrary rank. This allows us to derive the classification on the spaces SL(n,R)/SO(n) and to reduce the problem on a reducible space to the classification on each one of its factors.

differential geometry

Audience: researchers in the topic

( video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Riemannian geometry.

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, send a message to geometrywithsymmetries@gmail.com requiring it.

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