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Published in:
2016 | OriginalPaper | Chapter
The Symplectic Critical Surfaces in a Kähler Surface
Authors : Xiaoli Han, Jiayu Li, Jun Sun
Published in: Geometry and Topology of Manifolds
Publisher: Springer Japan
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Abstract
In this paper, we study the functional \(L_\beta =\int _\varSigma \frac{1}{\cos ^\beta \alpha }d\mu ,~\beta \ne -1\) in the class of symplectic surfaces. We derive the Euler-Lagrange equation. We call such a critical surface a \(\beta \)-symplectic critical surface. When \(\beta =0\), it is the equation of minimal surfaces. When \(\beta \ne 0\), a minimal surface with constant Kähler angle satisfies this equation, especially, a holomorphic curve or a special Lagrangian surface satisfies this equation. We study the properties of the \(\beta \)-symplectic critical surfaces.