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- Title
Parallel and totally umbilical hypersurfaces of the four‐dimensional Thurston geometry Sol04$\text{Sol}^4_0$.
- Authors
D'haene, Marie; Inoguchi, Jun‐ichi; Van der Veken, Joeri
- Abstract
We study hypersurfaces of the four‐dimensional Thurston geometry Sol04$\mathrm{Sol}^4_0$, which is a Riemannian homogeneous space and a solvable Lie group. In particular, we give a full classification of hypersurfaces whose second fundamental form is a Codazzi tensor—including totally geodesic hypersurfaces and hypersurfaces with parallel second fundamental form—and of totally umbilical hypersurfaces of Sol04$\mathrm{Sol}^4_0$. We also give a closed expression for the Riemann curvature tensor of Sol04$\mathrm{Sol}^4_0$, using two integrable complex structures.
- Subjects
HYPERSURFACES; SOLVABLE groups; GEOMETRY; RIEMANNIAN manifolds; HOMOGENEOUS spaces; SUBMANIFOLDS; LIE groups
- Publication
Mathematische Nachrichten, 2024, Vol 297, Issue 5, p1879
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.202300372