Lecture 6: J-holomorphic Curves and Applications

نویسنده

  • WEIMIN CHEN
چکیده

Let (M,ω) be a symplectic manifold of dimension 2n, and let J ∈ J (M,ω) be an ω-compatible almost complex structure. Let gJ(·, ·) ≡ ω(·, J ·) be the corresponding hermitian metric (i.e. J-invariant Riemannian metric) on M . Let (Σ, j) be a Riemann surface (not necessarily compact) with complex structure j. A smooth map u : Σ → M is called a (J, j)-holomorphic map (or simply a J-holomorphic map) if du ◦ j = J ◦ du, or equivalently, ∂̄J(u) ≡ 1 2 (du+ J ◦ du ◦ j) = 0.

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تاریخ انتشار 2007