dc.contributor.author |
Grosjean, Jean-Francois |
en |
dc.contributor.author |
Nagy, Paul-Andi |
en |
dc.date.accessioned |
2009-08-28T03:21:07Z |
en |
dc.date.available |
2009-08-28T03:21:07Z |
en |
dc.date.issued |
2006-05 |
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dc.identifier.citation |
Department of Mathematics - Research Reports-549 (2006) |
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dc.identifier.issn |
1173-0889 |
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dc.identifier.uri |
http://hdl.handle.net/2292/5010 |
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dc.description.abstract |
We investigate harmonic forms of geometrically formal metrics, which are defined as those having the exterior product of any two harmonic forms still harmonic. We prove that a formal Sasakian metric can exist only on a real cohomology sphere and that holomorphic forms of a formal K"ahler metric are parallel w.r.t. the Levi-Civita connection. In the general Riemannian case a formal metric with maximal second Betti number is shown to be flat . Finally we prove that a six-dimensional manifold with $b_1 neq 1, b_2 ge 3$ and not having the cohomology algebra of $mathbb{T}^3 times S^3$ carries a symplectic structure as soon as it admits a formal metric. |
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dc.publisher |
Department of Mathematics, The University of Auckland, New Zealand |
en |
dc.relation.ispartofseries |
Research Reports - Department of Mathematics |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
en |
dc.source.uri |
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=549 |
en |
dc.title |
Holomorphic forms of geometrically formal Kaehler manifolds |
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dc.type |
Technical Report |
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dc.subject.marsden |
Fields of Research::230000 Mathematical Sciences::230100 Mathematics |
en |
dc.rights.holder |
The author(s) |
en |