The symplectic critical surfaces in a kähler surface

Abstract

In this paper, we study the functional (formula presented), 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 Kahler 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.