The structure of pseudo - holomorphic subvarieties for a degenerate almost complex structure and symplectic form on S 1 B 3
نویسنده
چکیده
A self-dual harmonic 2{form on a 4{dimensional Riemannian manifold is symplectic where it does not vanish. Furthermore, away from the form’s zero set, the metric and the 2{form give a compatible almost complex structure and thus pseudo-holomorphic subvarieties. Such a subvariety is said to have nite energy when the integral over the variety of the given self-dual 2{form is nite. This article proves a regularity theorem for such nite energy subvarieties when the metric is particularly simple near the form’s zero set. To be more precise, this article’s main result asserts the following: Assume that the zero set of the form is non-degenerate and that the metric near the zero set has a certain canonical form. Then, except possibly for a nite set of points on the zero set, each point on the zero set has a ball neighborhood which intersects the subvariety as a nite set of components, and the closure of each component is a real analytically embedded half disk whose boundary coincides with the zero set of the form. AMS Classi cation numbers Primary: 53C07
منابع مشابه
The structure of pseudo - holomorphic subvarieties for a degenerate almost complex structure and symplectic form on S 1 × B 3 Clifford
A self-dual harmonic 2–form on a 4–dimensional Riemannian manifold is symplectic where it does not vanish. Furthermore, away from the form’s zero set, the metric and the 2–form give a compatible almost complex structure and thus pseudo-holomorphic subvarieties. Such a subvariety is said to have finite energy when the integral over the variety of the given self-dual 2–form is finite. This articl...
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