International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 47, Pages 3015-3022
Three theorems on cosymplectic hypersurfaces of six-dimensional
Hermitian submanifolds of the Cayley algebra
1Department of Mathematics, Applied Science University, Amman 11931, Jordan
2Department of Computer Technologies, Smolensk University of Humanities, Smolensk 214014, Russia
Received 1 June 2002
Copyright © 2003 Ahmad Al-Othman and M. Banaru. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 to be a minimal submanifold
of is established. It is also proved that a six-dimensional
Hermitian submanifold satisfying the -cosymplectic
hypersurfaces axiom is a Kählerian manifold.