Curvature properties of Lie hypersurfaces in the complex hyperbolic space
Tatsuyoshi Hamada, Yuji Hoshikawa, Hiroshi Tamaru
TL;DR
This paper investigates the intrinsic curvature properties of Lie hypersurfaces in complex hyperbolic space, revealing their geometric deformation from minimal ruled hypersurfaces to horospheres.
Contribution
It provides a detailed analysis of Ricci, scalar, and sectional curvatures of Lie hypersurfaces, enhancing understanding of their geometric structure.
Findings
Characterization of Ricci curvatures
Formulas for scalar curvatures
Analysis of sectional curvatures
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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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Algebra and Geometry