On stability of Hermitian structures on 6-dimensional planar submanifolds of Cayley algebra

Abstract

We consider 6-dimensional planar submanifolds of Cayley algebra. As it is known, the so-called Brown — Gray three-fold vector cross prod­ucts induce almost Hermitian structures on such submanifolds. We select the case when the almost Hermitian structures on 6-dimensional planar submanifolds of Cayley algebra are Hermitian, i. e. these structures are in­tegrable. It is proved that the Hermitian structure on a 6-dimensional planar submanifold of Cayley algebra is stable if and only if such submanifold is totally geodesic.