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Conformally related Kähler metrics and the holonomy of lcK manifolds

Madani, Farid ; Moroianu, Andrei ; Pilca, Mihaela



Abstract

A locally conformally Kahler (lcK) manifold is a complex manifold (M, J) together with a Hermitian metric g which is conformal to a Kahler metric in the neighbourhood of each point. In this paper we obtain three classification results in locally conformally Kahler geometry. The first one is the classification of conformal classes on compact manifolds containing two nonhomothetic Kahler metrics. ...

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