Sectional curvatures of ruled real hypersurfaces in a complex hyperbolic space

A ruled real hypersurface in a nonflat complex space form M˜n(c)(n≥2) of constant holomorphic sectional curvature c(≠0) is, in a word, a real hypersurface having a foliation by totally geodesic complex hyperplanes M˜n−1(c). In this paper, we investigate the sectional curvatures K of ruled real hyper...

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Bibliographic Details
Published in:Differential geometry and its applications 2017-04, Vol.51, p.1-8
Main Authors: Maeda, Sadahiro, Tanabe, Hiromasa
Format: Article
Language:English
Subjects:
Complex hyperbolic space
Ruled real hypersurfaces
Sectional curvatures
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Summary:A ruled real hypersurface in a nonflat complex space form M˜n(c)(n≥2) of constant holomorphic sectional curvature c(≠0) is, in a word, a real hypersurface having a foliation by totally geodesic complex hyperplanes M˜n−1(c). In this paper, we investigate the sectional curvatures K of ruled real hypersurfaces in a complex hyperbolic space and show that such hypersurfaces are classified into two types with regard to the range of K.
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2016.11.007