Symplectic Critical Surfaces in Kähler Surfaces
نویسندگان
چکیده
Let M be a Kähler surface and Σ be a closed symplectic surface which is smoothly immersed in M . Let α be the Kähler angle of Σ in M . We first deduce the Euler-Lagrange equation of the functional L = ∫ Σ 1 cosα dμ in the class of symplectic surfaces. It is cos αH = (J(J∇ cosα)), where H is the mean curvature vector of Σ in M , J is the complex structure compatible with the Kähler form ω in M , which is an elliptic equation. We then study the properties of the equation.
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