Geometric Properties of Lie Hypersurfaces in a Complex Hyperbolic Space

We study homogeneous real hypersurfaces having no focal submanifolds in a complex hyperbolic space. They are called Lie hypersurfaces in this space. We clarify the geometry of Lie hypersurfaces in terms of their sectional curvatures, the behavior of the characteristic vector field and their holomorp...

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Bibliographic Details
Published in:Czechoslovak mathematical journal 2019-12, Vol.69 (4), p.983-996
Main Authors: Kim, Young Ho, Maeda, Sadahiro, Tanabe, Hiromasa
Format: Article
Language:English
Subjects:
Analysis
Convex and Discrete Geometry
Fields (mathematics)
Hyperspaces
Manifolds (mathematics)
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
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Summary:We study homogeneous real hypersurfaces having no focal submanifolds in a complex hyperbolic space. They are called Lie hypersurfaces in this space. We clarify the geometry of Lie hypersurfaces in terms of their sectional curvatures, the behavior of the characteristic vector field and their holomorphic distributions.
ISSN:0011-4642
1572-9141
DOI:10.21136/CMJ.2019.0565-17