On products of harmonic forms
Differential Geometry
2007-05-23 v2 Algebraic Geometry
Geometric Topology
Symplectic Geometry
Abstract
We prove that manifolds admitting a Riemannian metric for which products of harmonic forms are harmonic satisfy strong topological restrictions, some of which are akin to properties of flat manifolds. Others are more subtle, and are related to symplectic geometry and Seiberg-Witten theory. We also prove that a manifold admits a metric with harmonic forms whose product is not harmonic if and only if it is not a rational homology sphere.
Keywords
Cite
@article{arxiv.math/0004009,
title = {On products of harmonic forms},
author = {D. Kotschick},
journal= {arXiv preprint arXiv:math/0004009},
year = {2007}
}
Comments
Revised to include flatness of formal metrics on tori of arbitrary dimension