Madani, Farid and Moroianu, Andrei and Pilca, Mihaela (2020) Conformally related Kahler metrics and the holonomy of lcK manifolds. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 22 (1). pp. 119-149. ISSN 1435-9855,
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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. The second one is the classification of compact Einstein locally conformally Kahler manifolds. The third result is the classification of the possible (restricted) Riemannian holonomy groups of compact locally conformally Kahler manifolds. We show that every locally (but not globally) conformally Kahler compact manifold of dimension 2n has holonomy SO(2n), unless it is Vaisman, in which case it has restricted holonomy SO(2n - 1). We also show that the restricted holonomy of a proper globally conformally Kahler compact manifold of dimension 2n is either SO(2n), or SO(2n - 1), or U(n), and we give the complete description of the possible solutions in the last two cases.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | HAMILTONIAN 2-FORMS; EINSTEIN; GEOMETRY; lcK structure; conformally Kahler structure; holonomy; Calabi Ansatz; Kahler structure; ambikahler structure |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Apr 2021 08:58 |
| Last Modified: | 07 Apr 2021 08:58 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45495 |
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