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Three theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra. (English) Zbl 1045.53037
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.
MSC:
53C40 Global submanifolds
53C55 Global differential geometry of Hermitian and Kählerian manifolds
17A35 Nonassociative division algebras
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