This article is cited in 3 papers

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

M. B. Banaru

Smolensk Humanitarian University

Abstract: 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.

UDC: 513.74

Received: 01.06.2001
Revised: 15.05.2002

DOI: 10.4213/mzm265

 English version: Mathematical Notes, 2003, 74:3, 311–315

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