Homogeneous hypersurfaces of the four-dimensional Thurston geometry ${\rm Sol_0^4}$
Differential Geometry
2025-11-03 v2
Abstract
In this paper, we classify hypersurfaces with constant principal curvatures in the four-dimensional Thurston geometry under certain geometric conditions. As an application of the classification result, we give a complete classification of homogeneous hypersurfaces in , which solves a problem raised by Erjavec and Inoguchi (Problem 6.4 of [J. Geom. Anal. 33, Art. 274, (2023)]).
Keywords
Cite
@article{arxiv.2508.10545,
title = {Homogeneous hypersurfaces of the four-dimensional Thurston geometry ${\rm Sol_0^4}$},
author = {Marie D'haene and Guoxin Wei and Zeke Yao and Xi Zhang},
journal= {arXiv preprint arXiv:2508.10545},
year = {2025}
}
Comments
18 pages. Comments are welcome