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On Four Dimensional Hermitian Manifolds

The present paper is devoted to 4-dimentional Hermitain manifold. We give a new necessary and sufficient condition of integrability and we introduce a new class of locally conformal Kähler manifolds that we consider a twin of the Vaisman ones. Then, some basic properties of this class is discussed, also the existence of such manifolds is shown with concrete examples.

Keywords:

Almost Hermitian manifolds, almost contact metric manifolds locally conformal Kähler manifolds,

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