On locally conformal Kähler structures
A locally conformal Kähler manifold is introduced in  as a Hermitian manifold whose metric is locally conformal to a Kähler metric. As a special case, a generalized Hopf manifold has been introduced, which is topologically different from a Kähler manifold if it is compact. In the first half of this paper, we will discuss the Riemannian curvature tensor of a generalized Hopf manifold in the case when holomorphic sectional curvature is constant except for a certain section. In the second half, we study a Riemannian manifold which admits more than one locally conformal Kähler structures with some relations.
KeywordsCurvature Tensor Betti Number Ricci Tensor Null Vector Hermitian Manifold
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