Homogeneous hypersurfaces of the four-dimensional Thurston geometries $\mathrm{Sol}_1^4$, $\mathrm{Sol}_{m,n}^4$ and $\mathrm{Nil}^4$

Xiaoge Lu; Zeke Yao; Xi Zhang

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arXiv · 2606.30257

Homogeneous hypersurfaces of the four-dimensional Thurston geometries $\mathrm{Sol}_1^4$, $\mathrm{Sol}_{m,n}^4$ and $\mathrm{Nil}^4$

Xiaoge Lu·Zeke Yao·Xi Zhang

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Abstract

In this paper, we focus on the four-dimensional Thurston geometries whose isometry groups are four-dimensional, namely $\mathrm{Sol}_1^4$, $\mathrm{Sol}_{m,n}^4$ and $\mathrm{Nil}^4$. We classify homogeneous hypersurfaces in the above three manifolds.

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Xiaoge Lu, Zeke Yao, Xi Zhang. 2026-06-29. Homogeneous hypersurfaces of the four-dimensional Thurston geometries $\mathrm{Sol}_1^4$, $\mathrm{Sol}_{m,n}^4$ and $\mathrm{Nil}^4$. https://arxiv.org/abs/2606.30257

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