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arXiv · 0711.2211

Symplectic critical surfaces in Kähler surfaces

Xiaoli Han·Jiayu Li
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Abstract

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 $L=\int_Σ\frac{1}{\cosα}dμ$ in the class of symplectic surfaces. It is $\cos^3αH=(J(J\nabla\cosα)^\top)^\bot$, 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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Xiaoli Han, Jiayu Li. 2007-11-14. Symplectic critical surfaces in Kähler surfaces. https://arxiv.org/abs/0711.2211

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