Symplectic critical surfaces in K\"ahler surfaces
Symplectic critical surfaces in K\"ahler surfaces
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DOI：
10.4171/jems/207
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发表时间：
2007-11
期刊：
影响因子：
--
通讯作者：
Xiaoling Han;Jiayu Li
中科院分区：
文献类型：
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作者：
Xiaoling Han;Jiayu Li
设$M$是K\“ahler曲面，$\Sigma$是光滑浸入$M$的闭辛曲面.设$\alpha$是$\Sigma$在$M$中的K\“ahler角。我们首先推导了辛曲面类中泛函L=\int_{\Sigma}\frac{1}{\cos\alpha}d\mu$的Euler-Lagrange方程。它是$\cos^3\alpha H=（J（J\nabla\cos\alpha）^\top）^\bot$，其中$H$是$\Sigma$在$M$中的平均曲率向量，$J$是与$M$中的K\“ahler形式$\omega$相容的复结构，这是一个椭圆方程。然后我们研究了方程的性质。
Let $M$ be a K\"ahler surface and $\Sigma$ be a closed symplectic surface which is smoothly immersed in $M$. Let $\alpha$ be the K\"ahler angle of $\Sigma$ in $M$. We first deduce the Euler-Lagrange equation of the functional $L=\int_{\Sigma}\frac{1}{\cos\alpha}d\mu$ in the class of symplectic surfaces. It is $\cos^3\alpha H=(J(J\nabla\cos\alpha)^\top)^\bot$, where $H$ is the mean curvature vector of $\Sigma$ in $M$, $J$ is the complex structure compatible with the K\"ahler form $\omega$ in $M$, which is an elliptic equation. We then study the properties of the equation.