On Six-Dimensional $G2$-Submanifolds of Cayley Algebras

M. B. Banaru

Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 323-328.

Résumé

It is proved that a generic-type 6-dimensional almost Hermitian submanifold of the algebra of octaves is minimal if and only if it belongs to the Gray–Hervella class $G2$. This is a maximal strengthening of the well-known result of Gray, who proved the minimality of the 6-dimensional Kähler submanifolds of the Cayley algebra.

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