Three theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra

Abstract

It is proved that cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the octave algebra are ruled manifolds. A necessary and sufficient condition for a cosymplectic hypersurface of a Hermitian submanifold M6⊂O to be a minimal submanifold of M6 is established. It is also proved that a six-dimensional Hermitian submanifold M6⊂O satisfying the g-cosymplectic hypersurfaces axiom is a Kählerian manifold.