Geodesic
Geometric properties of Lie hypersurfaces in a complex hyperbolic space
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 983-996.

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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.
DOI : 10.21136/CMJ.2019.0565-17
Classification : 53B25, 53C40
Keywords: complex hyperbolic space; homogeneous real hypersurface; Lie hypersurface; homogeneous ruled real hypersurface; equidistant hypersurface; horosphere; sectional curvature; shape operator; integral curve of the characteristic vector field; holomorphic distributions; homogeneous curve 
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Kim, Young Ho; Maeda, Sadahiro; Tanabe, Hiromasa. Geometric properties of Lie hypersurfaces in a complex hyperbolic space. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 983-996. doi : 10.21136/CMJ.2019.0565-17. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0565-17/

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