CR-hypersurfaces of a conformal Kenmotsu manifold satisfying certain shape operator conditions
type: Item
instance of: scholarly article
title: CR-hypersurfaces of a conformal Kenmotsu manifold satisfying certain shape operator conditions
zbMATH Open document ID: 1389.53070
author: Peng Zhang
published in: Periodica Mathematica Hungarica
publication date: 2017-11-10T00:00:00Z
review text: In the reviewed paper the authors introduce conformal Kenmotsu manifolds. A smooth manifold \(M^{2n+1}\) with an almost contact metric structure \((\phi,\eta,\xi,g)\) is called a conformal Kenmotsu manifold if there is a positive smooth function \(f\colon M\to\mathbb R\) such that \(\tilde{g}=\mathrm{exp}(f)g\), \(\tilde{\xi}=(\mathrm{exp}(-f))^{\frac 12}\xi\), \(\tilde{\eta}= (\mathrm{exp}(f))^{\frac 12}\eta\), \(\tilde{\phi}=\phi\), is a Kenmotsu structure on \(M\). Next the authors investigate CR-hypersurfaces of conformal Kenmotsu manifolds. First they consider CR-hypersurfaces with a parallel shape operator. The authors prove that if such hypersurface is tangent to the Lie vector field \(\omega^\sharp=\mathrm{grad}\,f\), then it is totally geodesic, and if it is normal to \(\omega^\sharp\), then it is totally umbilic. Finally the authors construct a 3-dimensional example of a conformal Kenmotsu manifold which is not Kenmotsu.
reviewed by: Marian Hotloś
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 6806100
zbMATH Keywords: Kenmotsu manifold
zbMATH Keywords: conformal Kenmotsu manifold
MaRDI profile type: Publication
full work available at URL: s10998-016-0131-6
OpenAlex ID: W2269149151
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DOI: 10.1007/S10998-016-0131-6
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description: scientific article; zbMATH DE number 6806100