Obstructions to the existence of Kähler structures on compact complex manifolds
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Abstract:
We prove that a manifold in the Fujiki class ${\mathcal C}$ which supports a $i\partial \bar \partial$-closed metric is Kähler. This result implies that on a compact complex manifold in the Fujiki class ${\mathcal C}$ which is not Kähler there exists a nonzero $i\partial \bar \partial$-exact, positive current of bidimension $(1,1)$.References
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Additional Information
- Ionuţ Chiose
- Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 014700, Romania
- Email: Ionut.Chiose@imar.ro
- Received by editor(s): November 6, 2012
- Published electronically: July 3, 2014
- Additional Notes: The author was supported by a Marie Curie International Reintegration Grant within the $7^\textrm {th}$ European Community Framework Programme and the CNCS grant PN-II-ID-PCE-2011-3-0269
- Communicated by: Lei Ni
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 3561-3568
- MSC (2010): Primary 32J27; Secondary 32Q15
- DOI: https://doi.org/10.1090/S0002-9939-2014-12128-9
- MathSciNet review: 3238431