The monopole equations and $J$-holomorphic curves on weakly convex almost Kähler 4-manifolds
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Abstract:
We prove that a weakly convex almost Kähler 4-manifold contains a compact, non-constant $J$-holomorphic curve if the corresponding monopole invariant is not zero and if the corresponding line bundle is non-trivial.References
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Additional Information
- Yutaka Kanda
- Affiliation: Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan
- Email: kanda@math.sci.hokudai.ac.jp
- Received by editor(s): March 8, 1999
- Received by editor(s) in revised form: February 28, 2000
- Published electronically: February 15, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 2215-2243
- MSC (2000): Primary 57R57
- DOI: https://doi.org/10.1090/S0002-9947-01-02697-6
- MathSciNet review: 1814068