Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank

2022/02/10 by José Carlos Díaz-Ramos, Diaz-Ramos, Jose Carlos, Miguel Domínguez-Vázquez +3 · 2 citations
Mathematics · #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2202.05138

Abstract

We develop a new structural result for cohomogeneity one actions on (not necessarily irreducible) symmetric spaces of noncompact type and arbitrary rank. We apply this result to classify cohomogeneity one actions on SL(n,R)/SO(n), n>1, up to orbit equivalence. We also reduce the classification problem on a reducible space to the classification on each one of its irreducible factors, which in particular allows to classify cohomogeneity one actions on any finite product of hyperbolic spaces.

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• On Hopf hypersurfaces of the complex hyperbolic quadric with constant principal curvatures
• Homogeneous hypersurfaces of the four-dimensional Thurston geometry \rm Sol₀⁴

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