Oriented 6-dimensional submanifolds in the octonions. III (Q1345786)

[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 \(O\).