Local Properties of Self-Dual Harmonic 2-forms on a 4-Manifold

1997/05/30 by Ko Honda, Honda, Ko
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9705010

9 pages, LaTex

arxiv created 1997/05/31 · arxiv updated 2009/11/30

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 S¹× S², after a slight modification, must be one of two possibilities.

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