Curvature surfaces of Hopf hypersurfaces in complex space forms
type: Item
instance of: scholarly article
title: Curvature surfaces of Hopf hypersurfaces in complex space forms
zbMATH Open document ID: 0857.53013
DOI: 10.1007/BF02570486
author: Rolf Böning
published in: Manuscripta Mathematica
publication date: 1995-12-10T00:00:00Z
full work available at URL: https://eudml.org/doc/156099
review text: Let \(N\) be the \(n\)-dimensional complex projective or complex hyperbolic space of constant holomorphic curvature \(\pm 4\) and denote its complex structure by \(J\). Furthermore, let \(M\) be a Hopf hypersurface of \(N\), i.e., \(M\) is a real hypersurface with a global unit normal field \(\eta\) whose structure field \(U := -J\eta\) is principal. In the present article the author thoroughly investigates the behaviour of the other principal curvatures of \(M\). In particular, he examines the integrability of the principal distributions and the geometry of their integral foliations. Often they turn out to be totally real; then they have the properties known from hypersurfaces of real space forms. The results are used to classify Hopf hypersurfaces with three principal curvatures.
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 824171
zbMATH Keywords: complex space forms
zbMATH Keywords: real hypersurfaces
zbMATH Keywords: principal curvatures
reviewed by: Helmut Reckziegel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 824171