Al-Othman, Ahmad; Banaru, M. Three theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra. (English) Zbl 1045.53037 Int. J. Math. Math. Sci. 2003, No. 47, 3015-3022 (2003). 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. Reviewer: Radu Iordănescu (Bucureşti) MSC: 53C40 Global submanifolds 53C55 Global differential geometry of Hermitian and Kählerian manifolds 53D15 Almost contact and almost symplectic manifolds Keywords:cosymplectic hypersurfaces; octave algebra; Hermitian submanifold PDFBibTeX XMLCite \textit{A. Al-Othman} and \textit{M. Banaru}, Int. J. Math. Math. Sci. 2003, No. 47, 3015--3022 (2003; Zbl 1045.53037) Full Text: DOI EuDML