Oriented 6-dimensional submanifolds in the octonions. III
type: Item
instance of: scholarly article
title: Oriented 6-dimensional submanifolds in the octonions. III
zbMATH Open document ID: 0827.53044
DOI: 10.1155/S0161171295000159
author: Hideya Hashimoto
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1995-12-13T00:00:00Z
full work available at URL: https://eudml.org/doc/47305
full work available at URL: issue-1.html
review text: [For part II see the author, Geometry of manifolds, Coll. Pap. 35th Symp. Differ. Geom., Matsumoto/Japan 1988, Perspect. Math. 8, 71-94 (1989; Zbl 0712.53024)]. It is known that the octonions \(O\) are considered as the algebra \(H \oplus H\) where \(H\) denotes the quaternions. According to this consideration, the author classifies 6-dimensional almost Hermitian submanifolds in \(O\) using the classification introduced by \textit{A. Gray} and the reviewer [Ann. Mat. Pura Appl., IV. Ser. 123, 35-58 (1980; Zbl 0444.53032)]. In the second part of this paper he gives an interesting example of quasi-Kähler submanifolds in \(O\) whose normal connections are non-flat and also study weakly \(*\)-Einstein submanifolds in \(O\).
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 733303
zbMATH Keywords: Einstein submanifolds
zbMATH Keywords: octonians
zbMATH Keywords: 6-dimensional almost Hermitian submanifolds
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 733303