Homogeneous hypersurfaces of the four-dimensional Thurston geometry ${\rm Sol_0^4}$

Marie D'haene; Guoxin Wei; Zeke Yao; Xi Zhang

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arXiv · 2508.10545

Homogeneous hypersurfaces of the four-dimensional Thurston geometry ${\rm Sol_0^4}$

Marie D'haene·Guoxin Wei·Zeke Yao·Xi Zhang

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Abstract

In this paper, we classify hypersurfaces with constant principal curvatures in the four-dimensional Thurston geometry ${\rm Sol_0^4}$ under certain geometric conditions. As an application of the classification result, we give a complete classification of homogeneous hypersurfaces in ${\rm Sol_0^4}$, which solves a problem raised by Erjavec and Inoguchi (Problem 6.4 of [J. Geom. Anal. 33, Art. 274, (2023)]).

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Marie D'haene, Guoxin Wei, Zeke Yao, Xi Zhang. 2025-08-14. Homogeneous hypersurfaces of the four-dimensional Thurston geometry ${\rm Sol_0^4}$. https://arxiv.org/abs/2508.10545

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