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arXiv · 0908.3419

Curvature properties of Lie hypersurfaces in the complex hyperbolic space

Tatsuyoshi Hamada·Yuji Hoshikawa·Hiroshi Tamaru
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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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Tatsuyoshi Hamada, Yuji Hoshikawa, Hiroshi Tamaru. 2009-08-24. Curvature properties of Lie hypersurfaces in the complex hyperbolic space. https://arxiv.org/abs/0908.3419

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