Local Properties of Self-Dual Harmonic 2-forms on a 4-Manifold
dg-ga
2008-02-03 v2 Differential Geometry
Abstract
We will prove a Moser-type theorem for self-dual harmonic 2-forms on closed 4-manifolds, and use it to classify local forms on neighborhoods of singular circles on which the 2-form vanishes. Removing neighborhoods of the circles, we obtain a symplectic manifold with contact boundary - we show that the contact form on each S^1\times S^2, after a slight modification, must be one of two possibilities.
Keywords
Cite
@article{arxiv.dg-ga/9705010,
title = {Local Properties of Self-Dual Harmonic 2-forms on a 4-Manifold},
author = {Ko Honda},
journal= {arXiv preprint arXiv:dg-ga/9705010},
year = {2008}
}
Comments
9 pages, LaTex