Remarks on the product of harmonic forms

Liviu Ornea, Mihaela Pilca

Published 2010-01-13Version 1

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 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 necessary and sufficicient conditions for a Vaisman metric to be formal.