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Remarks on the
product of harmonic forms
Liviu Ornea and Mihaela Pilca |
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Vol. 250 (2011), No. 2, 353–363
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Abstract |
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A metric is formal if all products of harmonic forms are again harmonic. The existence of a formal metric implies Sullivan formality of the manifold, and hence formal metrics can exist only in the presence of a very restricted topology. We show that a warped product metric is formal if and only if the warping function is constant and derive further topological obstructions to the existence of formal metrics. In particular, we determine the necessary and sufficient conditions for a Vaisman metric to be formal. |
Keywords
formality, harmonic form, warped product, Vaisman manifold,
Betti numbers
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Mathematical Subject Classification 2000
Primary: 53C25
Secondary: 53C55, 58A14
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Milestones
Received: 19 January 2010
Revised: 11 October 2010
Accepted: 16 November 2010
Published: 31 March 2011
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Authors |
| Liviu Ornea | |
| Faculty of Mathematics University of Bucharest Str Academiei nr 14 RO-010014 Bucharest Romania |
Institute of Mathematics “Simion
Stoilow” of the Romanian Academy Calea Grivitei nr 21 RO-010702 Bucharest Romania |
| Mihaela Pilca | |
| Fakultät für Mathematik University of Regensburg Universitätsstr. 31 D-93053 Regensburg Germany |
Institute of Mathematics “Simion
Stoilow” of the Romanian Academy Calea Grivitei nr 21 RO-010702 Bucharest Romania |
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