Khler曲面上的辛临界曲面

The symplectic critical surfaces in a Khler surface

本文在辛曲面类中研究了泛函Lβ=∫Σ1cos^βαdμ,β≠-1.之前的研究曾推导了它的EulerLagrange方程,并把满足这个方程的曲面称为β辛临界曲面.当β=0时,得到的是极小曲面方程;当β≠0时,常Khler角极小曲面满足这个方程.特别地,全纯曲线或特殊Lagrange曲面满足这个方程.本文研究β辛临界曲面的一些性质.

In this paper, we study the functional Lβ =Σ1cos~βαdμ, β≠-1 in the class of symplectic surfaces.We derive the Euler-Lagrange equation. We call such a critical surface a β-symplectic critical surface. When β = 0, it is the equation of minimal surfaces. When β≠ 0, a minimal surface with constant Khler angle satisfies this equation. Especially, a holomorphic curve or a special Lagrangian surface satisfies this equation. We study the properties of the β-symplectic critical surfaces.