Generating Curves of Minimal Ruled Real Hypersurfaces in a Nonflat Complex Space Form

We first provide a necessary and sufficient condition for a ruled real hypersurface in a nonflat complex space form to have constant mean curvature in terms of integral curves of the characteristic vector field on it. This yields a characterization of minimal ruled real hypersurfaces by circles. We...

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Bibliographic Details
Published in:Canadian mathematical bulletin 2019-06, Vol.62 (2), p.383-392
Main Authors: Maeda, Sadahiro, Tanabe, Hiromasa, Udagawa, Seiichi
Format: Article
Language:English
Subjects:
Fields (mathematics)
Hyperspaces
Mathematics
Vector space
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Summary:We first provide a necessary and sufficient condition for a ruled real hypersurface in a nonflat complex space form to have constant mean curvature in terms of integral curves of the characteristic vector field on it. This yields a characterization of minimal ruled real hypersurfaces by circles. We next characterize the homogeneous minimal ruled real hypersurface in a complex hyperbolic space by using the notion of strong congruency of curves.
ISSN:0008-4395
1496-4287
DOI:10.4153/CMB-2018-032-6