Real hypersurfaces in quaternionic projective space
type: Item
instance of: scholarly article
title: Real hypersurfaces in quaternionic projective space
zbMATH Open document ID: 0615.53012
DOI: 10.1007/BF01790548
author: Yanyan Li
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1986-01-01T00:00:00Z
review text: The paper is a systematic study of real hypersurfaces of quaternionic projective spaces via the focal set theory. By using the induced structures on a real hypersurface the authors obtain three classes of real hypersurfaces. Then by means of one of these classes they find an example of a proper quaternion CR-submanifold in the sense of \textit{M. Barros}, \textit{B. Y. Chen} and \textit{F. Urbano} [Kodai Math. J. 4, 399-417 (1981; Zbl 0481.53046)]. In the last part of the paper the authors obtain classification theorems for the following classes of real hypersurfaces: a) real hypersurfaces with constant principal curvatures and CR-structure in the sense of the reviewer [Chin. J. Math. 14, 81-94 (1986; Zbl 0602.53037)], b) real hypersurfaces with two distinct principal curvatures, c) pseudo-Einstein and almost Einstein real hypersurfaces.
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 3996538
zbMATH Keywords: Einstein spaces
zbMATH Keywords: real hypersurfaces
zbMATH Keywords: quaternionic projective spaces
zbMATH Keywords: focal set
zbMATH Keywords: quaternion CR-submanifold
zbMATH Keywords: principal curvatures
zbMATH Keywords: CR-structure
reviewed by: Aurel Bejancu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3996538