On real hypersurfaces in quaternionic projective space with \({\mathcal D}^\perp\)-recurrent second fundamental tensor
type: Item
instance of: scholarly article
title: On real hypersurfaces in quaternionic projective space with \({\mathcal D}^\perp\)-recurrent second fundamental tensor
zbMATH Open document ID: 0915.53009
DOI: 10.1155/S0161171299221096
author: Young Jin Suh
author: Juan D. Pérez
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1999-04-13T00:00:00Z
full work available at URL: https://eudml.org/doc/48167
full work available at URL: issue-1.html
review text: Let \(M\) be a real hypersurface in quaternionic projective space \(QP^m\), \(m\geq 3\), and denote by \((\phi_i, \xi_i, \eta_i,g)\), \(i=1,2,3\), the local almost contact metric structures on \(M\) which are induced by some canonical local basis of the quaternionic Kähler structure of \(QP^m\). Moreover, denote by \(A\) the shape operator of \(M\), by \(\nabla\) the Levi Civita covariant derivative of \(M\), and by \(D\) the maximal quaternionic subbundle of \(TM\). The authors classify all real hypersurfaces in \(QP^m\) which satisfy \(g((\nabla_X A)Y,Z)= \alpha(X) g(AY,Z)\) for some one-form \(\alpha\) on \(D\) and \(g((A\phi_i- \phi_iA)X,Y)=0\) for all \(X,Y,Z\in D\). They show that such a hypersurface \(M\) is either congruent to a tube around some totally geodesic \(QP^k\subset QP^m\) for some \(k\in \{0,\dots, m-1\}\) or \(M\) is ruled.
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 1275564
zbMATH Keywords: quaternionic projective space
zbMATH Keywords: shape operator
zbMATH Keywords: real hypersurfaces
reviewed by: Jürgen Berndt
MaRDI profile type: Publication
OpenAlex ID: W2069773348
description: scientific article; zbMATH DE number 1275564