Real hypersurfaces in complex two-plane Grassmannians with recurrent shape operator
type: Item
instance of: scholarly article
title: Real hypersurfaces in complex two-plane Grassmannians with recurrent shape operator
zbMATH Open document ID: 1218.53055
author: Seonhui Kim
author: Hae Young Yang
author: Hyunjin Lee
published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series
publication date: 2011-05-23T00:00:00Z
full work available at URL: https://eudml.org/doc/244381
full work available at URL: vol34 2 9.html
review text: A real hypersurface \(M\) in a complex two-plane Grassmannians \(G_{2}({\mathbb C}^{m+2})\) is a Hopf recurrent hypersurface if the Hopf foliation of \(M\) is totally geodesic and the shape operator \(A\) satisfies the recurrence relation \[ (\nabla _{X}A)Y=\omega (X)AY \] for a nonzero recurrence \(1\)-form \(\omega \). In this paper, the authors prove that there exist no Hopf recurrent hypersurfaces in the complex two-plane Grassmannians \(G_{2}({\mathbb C}^{m+2})\), \(m\geq 3\).
reviewed by: Mukut Mani Tripathi
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 5899041
zbMATH Keywords: real hypersurface
zbMATH Keywords: complex two-plane Grassmannians
zbMATH Keywords: Hopf hypersurface
zbMATH Keywords: recurrent shape operator
zbMATH Keywords: recurrent hypersurface
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5899041