The monopole equations and -holomorphic curves on weakly convex almost Kähler 4-manifolds

Author:
Yutaka Kanda

Journal:
Trans. Amer. Math. Soc. **353** (2001), 2215-2243

MSC (2000):
Primary 57R57

DOI:
https://doi.org/10.1090/S0002-9947-01-02697-6

Published electronically:
February 15, 2001

MathSciNet review:
1814068

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Abstract | References | Similar Articles | Additional Information

We prove that a weakly convex almost Kähler 4-manifold contains a compact, non-constant -holomorphic curve if the corresponding monopole invariant is not zero and if the corresponding line bundle is non-trivial.

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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

DOI:
https://doi.org/10.1090/S0002-9947-01-02697-6

Keywords:
Symplectic structure,
monopole equation,
$J$-holomorphic curve

Received by editor(s):
March 8, 1999

Received by editor(s) in revised form:
February 28, 2000

Published electronically:
February 15, 2001

Article copyright:
© Copyright 2001
American Mathematical Society