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Geometry and Topology of Manifolds pp 185–193Cite as

The Symplectic Critical Surfaces in a Kähler Surface

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 154))

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.

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References

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Acknowledgments

The research was supported by the National Natural Science Foundation of China, No.11131007, No.11471014, No. 11401440, 11426236.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China

    Xiaoli Han

  2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, People’s Republic of China

    Jiayu Li

  3. AMSS CAS, Beijing, 100190, People’s Republic of China

    Jiayu Li

  4. School of Mathematical Sciences, Wuhan University, Wuhan, 430072, People’s Republic of China

    Jun Sun

Authors
  1. Xiaoli Han
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  2. Jiayu Li
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  3. Jun Sun
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Corresponding author

Correspondence to Jiayu Li .

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Editors and Affiliations

  1. The University of Tokyo, Meguro-ku, Tokyo, Japan

    Akito Futaki

  2. Mathematical Institute, Tohoku University, Sendai,Aoba-ku, Japan

    Reiko Miyaoka

  3. School of Mathematical Sciences, Beijing Normal University, Beijing, China

    Zizhou Tang

  4. Chern Institute of Mathematics, Nankai University, Tianjin, China

    Weiping Zhang

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Han, X., Li, J., Sun, J. (2016). The Symplectic Critical Surfaces in a Kähler Surface. In: Futaki, A., Miyaoka, R., Tang, Z., Zhang, W. (eds) Geometry and Topology of Manifolds. Springer Proceedings in Mathematics & Statistics, vol 154. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56021-0_10

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