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Pré-Publication, Document De Travail Année : 2006

On the cohomology algebra of some classes of geometrically formal manifolds

Paul-Andi Nagy
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Résumé

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 Kähler 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 $b_1 \neq 1, b_2 \geqslant 2$ 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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Dates et versions

hal-00101996 , version 1 (28-09-2006)

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  • HAL Id : hal-00101996 , version 1

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Jean-Francois Grosjean, Paul-Andi Nagy. On the cohomology algebra of some classes of geometrically formal manifolds. 2006. ⟨hal-00101996⟩
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