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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 47, Pages 3015-3022
http://dx.doi.org/10.1155/S0161171203206190

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 Hindawi Publishing Corporation. 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.

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 M6O to be a minimal submanifold of M6 is established. It is also proved that a six-dimensional Hermitian submanifold M6O satisfying the g-cosymplectic hypersurfaces axiom is a Kählerian manifold.