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Curvatures properties of Lie hypersurfaces in the complex hyperbolic space |
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| Authors: | Tatsuyoshi Hamada Yuji Hoshikawa Hiroshi Tamaru |
| Affiliation: | 1. Department of Applied Mathematics, Fukuoka University, Fukuoka, 814-0180, Tatsuyoshi Hamanda, Japan 2. JST, CREST, 5 Sanbancho, Chiyoda-ku, Tokyo, 102-0075, Japan 3. Department of Mathematics, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan 4. Takamatsu-Kita Junior High School, Takamatsu, Kagawa, 761-0121, Japan |
| Abstract: | A Lie hypersurface in the complex hyperbolic space is a homogeneous real hypersurface without focal submanifolds. The set of all Lie hypersurfaces in the complex hyperbolic space is bijective to a closed interval, which gives a deformation of homogeneous hypersurfaces from the ruled minimal one to the horosphere. In this paper, we study intrinsic geometry of Lie hypersurfaces, such as Ricci curvatures, scalar curvatures, and sectional curvatures. |
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