Ornea, Liviu and Pilca, Mihaela (2011) REMARKS ON THE PRODUCT OF HARMONIC FORMS. PACIFIC JOURNAL OF MATHEMATICS, 250 (2). pp. 353-363. ISSN 0030-8730,
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | KAHLER GEOMETRY; FORMALITY; MANIFOLDS; LENGTH; SPACES; formality; harmonic form; warped product; Vaisman manifold; Betti numbers |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 23 Jun 2020 07:10 |
| Last Modified: | 23 Jun 2020 07:10 |
| URI: | https://pred.uni-regensburg.de/id/eprint/21062 |
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