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Tsukuba Journal of Mathematics
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Other literature type . 1993
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Tsukuba Journal of Mathematics
Article . 1993 . Peer-reviewed
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On ruled real hypersurfaces in a complex space form

Authors: Ahn, Seong-Soo; Lee, Sung-Baik; Suh, Young-Jin;

On ruled real hypersurfaces in a complex space form

Abstract

A real hypersurface \(M\) of a complex space form \(N\) is said to be ruled if \(M\) is foliated by one-codimensional totally geodesic complex submanifolds of \(N\). The authors provide a sufficient condition for a real hypersurface in a non-flat complex space form to be ruled. Explicitly, let \(M\) be a connected real hypersurface in a non-flat complex space form of complex dimension \(\geq 3\) and \((\phi,\xi,\eta,g)\) the induced almost contact metric structure on \(M\). Denote by \(T_ 0\) the subbundle of \(TM\) consisting of all vectors perpendicular to \(\xi\) and by \(A\) the shape operator of \(M\). If \(g((\nabla_ X A)Y,Z)= 0\) and \(g((A\phi- \phi A)X,Y)= 0\) for all \(X,Y,Z\in T_ 0\) and if \(\xi\) is not a principal curvature vector of \(M\) somewhere, then \(M\) is ruled. The authors also discuss a particular example of a minimal ruled real hypersurface in complex hyperbolic space.

Related Organizations
Keywords

real hypersurface, Local submanifolds, almost contact metric structure, minimal ruled real hypersurface, Global differential geometry of Hermitian and Kählerian manifolds, complex hyperbolic space

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
22
Average
Top 10%
Average
Green
hybrid