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Special Hermitian manifolds and the 1-cosymplectic hypersurfaces axiom. (English) Zbl 1318.53012
A special Hermitian manifold is a Hermitian manifold whose Kähler form \(F\) satisfies \(\delta F=0\), where \(\delta\) is the codifferentiation operator. The main result of the paper is that if a special Hermitian manifold \(M\) satisfies the 1-cosymplectic hypersurfaces axiom (i.e., every point of \(M\) belongs to some cosymplectic hypersurface of type one), then \(M\) is a Kähler manifold.

MSC:
53B35 Local differential geometry of Hermitian and Kählerian structures
53B21 Methods of local Riemannian geometry
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