Adapted complex structures in a neighborhood of an isotropic embedding |
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Authors: | F. Loose |
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Affiliation: | 1. Mathematisches Institut, Universit?t Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany
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Abstract: | Let (X, ω) be a symplectic manifold and ι: M ? X an isotropic embedding, ι*ω = 0. The isotropie embedding theorem gives a local normal form of X in a neighborhood of M, in particular a natural potential α of ω, ?dα = ω. Now, given certain geometrical structures on M and on the symplectic normal bundle of M, in particular inducing a natural energy momentum function H in a neighborhood of M, we construct a natural complex structure J in a neighborhood of M satisfying certain initial conditions associated to the given initial data along M and satisfying the equation (in J): dc H = α. This generalizes a theorem of Guillemin-Stenzel and Lempert-Szöke in the Lagrangean case. |
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Keywords: | KeywordHeading" >Math Subject Classifications 53C15 |
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