Three theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra (Q1415154)

The authors prove 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 \(M^6\subset O\) to be a minimal submanifold of \(M^6\) is established. It is also proved that a six-dimensional Hermitian submanifold \(M^6\subset O\) satisfying the \(g\)-cosymplectic hypersurfaces axiom is a Kählerian manifold.