Homogeneous hypersurfaces of the four-dimensional Thurston geometry \rm Sol₀⁴

2025/08/14 by D'haene, Marie, Wei, Guoxin, Yao, Zeke +1
#53C30 #53C40 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.10545

Abstract

In this paper, we classify hypersurfaces with constant principal curvatures in the four-dimensional Thurston geometry \rm Sol₀⁴ under certain geometric conditions. As an application of the classification result, we give a complete classification of homogeneous hypersurfaces in \rm Sol₀⁴, which solves a problem raised by Erjavec and Inoguchi (Problem 6.4 of [J. Geom. Anal. 33, Art. 274, (2023)]).

Citations

• Polar actions on homogeneous 3-spaces
• Classification of cohomogeneity-one actions on symmetric spaces of noncompact type
• Isoparametric Hypersurfaces in product spaces of space forms
• Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank
• Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one symmetric spaces
• Cohomogeneity one actions on noncompact symmetric spaces of rank one

Related

• Thurston geometries in dimension four from a Riemannian perspective
• Curvature homogeneous hypersurfaces in space forms
• Parallel and totally geodesic hypersurfaces of non-reductive homogeneous\n four-manifolds
• Classical Notions and Problems in Thurston Geometries
• Homogeneous Hypersurfaces with Isotropy in Affine Four-space