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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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##### References:
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