New diagonal family plus decomposition theorem reduces cohomogeneity-one actions on mixed symmetric spaces to single-type cases.
Isoparametric hypersurfaces in $\mathbb{S}^{n}\times \mathbb{R}^{m}$ and $\mathbb{H}^{n}\times \mathbb{R}^{m}$
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We first show that every isoparametric hypersurface in $\mathbb{S}^{n}\times \mathbb{R}^{m}$ or $\mathbb{H}^{n}\times \mathbb{R}^{m}$ possesses a constant angle function with respect to the canonical product structure. Exploiting this rigidity, we achieve a complete classification of isoparametric and homogeneous hypersurfaces in these product spaces. Furthermore, we prove that an isoparametric hypersurface in $\mathbb{S}^{n}\times \mathbb{R}^{m}$ or $\mathbb{H}^{n}\times \mathbb{R}^{m}$ also has constant principal curvatures.
fields
math.DG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Classification of homogeneous hypersurfaces in Sol₁⁴, Sol_{m,n}⁴ and Nil⁴.
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Cohomogeneity one actions on symmetric spaces of mixed type
New diagonal family plus decomposition theorem reduces cohomogeneity-one actions on mixed symmetric spaces to single-type cases.
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Homogeneous hypersurfaces of the four-dimensional Thurston geometries $\mathrm{Sol}_1^4$, $\mathrm{Sol}_{m,n}^4$ and $\mathrm{Nil}^4$
Classification of homogeneous hypersurfaces in Sol₁⁴, Sol_{m,n}⁴ and Nil⁴.