On the Ricci tensor of a real hypersurface of quaternionic hyperbolic space
type: Item
instance of: scholarly article
title: On the Ricci tensor of a real hypersurface of quaternionic hyperbolic space
zbMATH Open document ID: 0879.53015
DOI: 10.1007/BF02677457
author: Miguel Ortega
author: Juan D. Pérez
published in: Manuscripta Mathematica
publication date: 1998-01-26T00:00:00Z
full work available at URL: https://eudml.org/doc/156285
review text: The authors first show that a real hypersurface in a quaternionic hyperbolic space \(QH^m\) \((m\geq 3)\) with at most two distinct principal curvatures at each point is an open subset of a geodesic hypersphere, or of a tube around some totally geodesic quaternionic hyperbolic hyperplane, or of a horosphere in \(QH^m\). They use this result to prove that each pseudo-Einstein resp. almost-Einstein real hypersurface of \(QH^m\) \((m\geq 3)\) is an open part of one of the above model spaces. As a consequence they get that there are no Einstein real hypersurfaces in \(QH^m\). It is already known that in the dual quaternionic projective space there exists an Einstein real hypersurface.
reviewed by: Jürgen Berndt
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 1038287
zbMATH Keywords: Einstein manifolds
zbMATH Keywords: quaternionic hyperbolic space
zbMATH Keywords: two distinct principal curvatures
zbMATH Keywords: real hypersurfaces
MaRDI profile type: Publication
cites work: Real hypersurfaces in quaternionic space forms.
cites work: Focal Sets and Real Hypersurfaces in Complexes Projective Space
cites work: Q4171259
cites work: Quaternion Kählerian manifolds and fibred Riemannian spaces with Sasakian $3$-structure
cites work: Q5565587
cites work: Pseudo-Einstein real hypersurfaces in complex space forms
cites work: Real hypersurfaces in quaternionic projective space
cites work: Real hypersurfaces of a complex hyperbolic space
cites work: The fundamental equations of a submersion
cites work: Real hypersurfaces in quaternionic Kaehlerian manifolds with constant $Q$-sectional curvature
description: scientific article; zbMATH DE number 1038287