Czechoslovak Mathematical Journal, Vol. 69, No. 4, pp. 983-996, 2019
Geometric properties of Lie hypersurfaces in a complex hyperbolic space
Young Ho Kim, Sadahiro Maeda, Hiromasa Tanabe
Received December 11, 2017. Published online February 15, 2019.
Abstract: 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.
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
Affiliations: Young Ho Kim, Department of Mathematics, Kyungpook National University, 80 Daehakro, Bukgu, Daegu, 41566, Korea, e-mail: firstname.lastname@example.org, Sadahiro Maeda, Department of Mathematics, Saga University, 1 Honjo-machi, Saga, 840-8502, Japan, e-mail: email@example.com, Hiromasa Tanabe, Department of Science, National Institute of Technology, Matsue College, 14-4 Nishiikumacho, Matsue, Shimane 690-8518, Japan, e-mail: firstname.lastname@example.org