Quasi-Einstein totally real submanifolds of the nearly Kähler 6-sphere
type: Item
instance of: scholarly article
title: Quasi-Einstein totally real submanifolds of the nearly Kähler 6-sphere
zbMATH Open document ID: 0990.53014
author: Ryszard Deszcz
author: Luc Vrancken
author: Franki Dillen
author: Leopold Verstraelen
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2002-08-12T00:00:00Z
review text: The authors investigate 3-dimensional totally real quasi-Einstein submanifolds of the nearly Kähler 6-sphere \(S^6\). (A submanifold in \(S^6\) is said to be totally real if the almost complex structure \(J\) on \(S^6\) interchanges the tangent and the normal space. An \(n\)-dimensional manifold whose Ricci tensor has an eigenvalue of multiplicity at least \(n-1\) is said to be quasi-Einstein.) Necessary and sufficient conditions for a totally real \(M_3 \subset S^6\) to be quasi-Einstein are derived, examples of these submanifolds are constructed by considering tubes with different radii. The results of this paper together with the classification theorems in \textit{F. Dillen} and \textit{L. Vrancken} [Trans. Am. Math. Soc. 348, 1633-1646 (1996; Zbl 0882.53017)] provide a complete classification of the totally real quasi-Einstein submanifolds of \(S^6\).
reviewed by: M. A. Malakhaltsev
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 1445638
zbMATH Keywords: quasi-Einstein manifold
zbMATH Keywords: almost complex structure
zbMATH Keywords: tube
zbMATH Keywords: nearly Kähler manifold
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178224715
OpenAlex ID: W2069083132
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DOI: 10.2748/TMJ/1178224715
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description: scientific article; zbMATH DE number 1445638