International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 47, Pages 3015-3022
doi:10.1155/S0161171203206190
Three theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra
Ahmad Al-Othman1
and M. Banaru2
1Department of Mathematics, Applied Science University, Amman 11931, Jordan
2Department of Computer Technologies, Smolensk University of Humanities, Smolensk 214014, Russia
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.