Cohomogeneity-one actions on symmetric spaces

Abstract: In this talk, I will report on recent developments on the classification of cohomogeneity-one actions on symmetric spaces. The focus will be on symmetric spaces of noncompact type and of "mixed type" (i.e. those whose universal cover splits as a nontrivial product $\widetilde{M}=M_+\times M_0\times M_-$, with $M_+$ of compact type, $M_0$ a Euclidean space, and $M_-$ of noncompact type). For the former spaces a complete classification was recently obtained by Sanmartín-López and Solonenko. For the latter, in an upcoming work with Ivan Solonenko and Hiroshi Tamaru, we show that cohomogeneity-one actions split with respect to the aforementioned decomposition, with the only exception of a family of "diagonal" actions (which we parameterize explicitly).

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

Virtual seminar on geometry with symmetries

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

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