This article is cited in 11 papers

The type number of the cosymplectic hypersurfaces of 6-dimensional Hermitian submanifolds of the Cayley algebra

M. B. Banaru

Smolensk Humanitarian University

Abstract: We study the 6-dimensional oriented submanifolds of the Cayley algebra which are endowed with the Hermitian structure induced by 3-folds vector cross products. We prove that the type number of a cosymplectic hypersurface of a 6-dimensional Hermitian submanifold of the Cayley algebra is at most 3 and that a 6-dimensional Kaehler submanifold of the octave algebra has no cosymplectic hypersurfaces with the type number greater than one.

Keywords: Cayley algebra, Hermitian manifold, hypersurface, cosymplectic structure, type number.

UDC: 513.82

Received: 20.11.2001
Revised: 23.09.2002

 English version: Siberian Mathematical Journal, 2003, 44:5, 765–773

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