Homogeneous hypersurfaces of the four-dimensional Thurston geometry ${\rm Sol_0^4}$
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915588054450176 |
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| author | D'haene, Marie Wei, Guoxin Yao, Zeke Zhang, Xi |
| author_facet | D'haene, Marie Wei, Guoxin Yao, Zeke Zhang, Xi |
| contents | 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)]). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homogeneous hypersurfaces of the four-dimensional Thurston geometry ${\rm Sol_0^4}$ D'haene, Marie Wei, Guoxin Yao, Zeke Zhang, Xi Differential Geometry 53C42, 53C40, 53C30 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)]). |
| title | Homogeneous hypersurfaces of the four-dimensional Thurston geometry ${\rm Sol_0^4}$ |
| topic | Differential Geometry 53C42, 53C40, 53C30 |
| url | https://arxiv.org/abs/2508.10545 |