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The Lagrangian surfaces with constant curvature in Q2

  • 1.

    School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

  • 2.

    Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei 230026, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.06.001
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  • Author Bio:

    LI Kang, male, born in 1986, PhD. Research field: differential geometry. E-mail: likang@mail.ustc.edu.cn

  • Corresponding author: HU Sen
  • Received Date: 06 November 2014
  • Accepted Date: 17 April 2015
  • Rev Recd Date: 17 April 2015
  • Publish Date: 30 June 2015
    Abstract

  • Abstract

    A class of H-minimal Lagrangian surfaces with constant curvature in Q2 was described, and an example was given of minimal Lagrangian S2 with Gaussian curvature K=2.

    Abstract

    A class of H-minimal Lagrangian surfaces with constant curvature in Q2 was described, and an example was given of minimal Lagrangian S2 with Gaussian curvature K=2.
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    • References(8)
  • [1]
    Castro I, Urbano F. Examples of unstable Hamiltonian-minimal Lagrangian tori in C2[J]. Compositio Math, 1998, 111: 1-14.
    [2]
    Schoen R, Wolfson J. Minimizing volume among Lagrangian submanifolds[C]// Proc Sympos Pure Math: Vol 65. Providence, RI: Amer Math Soc, 1999: 181-199.
    [3]
    Ma H, Schmies M. Examples of Hamiltonian stationary Lagrangian tori in CP2[J]. Geom Dedicata, 2006, 118: 173-183.
    [4]
    Mironov A E, Zuo D. On a family of conformally flat Hamiltonian minimal Lagrangian tori in CP3[J]. Int Math Res Not, 2008,2008: 10.1093/imrn/rnn078.
    [5]
    Jiao X X, Wang J. Totally real minimal surfaces in the complex hyperquadrics[J]. Diff Geo Appl, 2013, 31: 540-555.
    [6]
    Hu S, Chen Q, Xu X W. Construction of Lagrangian submanifolds in CPn[J]. Pacific Journal of Math, 2012, 258: 31-49.
    [7]
    Chern S S, Wolfson J. Minimal surfaces by moving frames[J]. Amer J Math, 1983, 105(1):59-83.
    [8]
    Yang K. Complete and Compact Minimal Surface[M]. Dordrecht: Kluwer Academic, 1989.
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    [1]
    Castro I, Urbano F. Examples of unstable Hamiltonian-minimal Lagrangian tori in C2[J]. Compositio Math, 1998, 111: 1-14.
    [2]
    Schoen R, Wolfson J. Minimizing volume among Lagrangian submanifolds[C]// Proc Sympos Pure Math: Vol 65. Providence, RI: Amer Math Soc, 1999: 181-199.
    [3]
    Ma H, Schmies M. Examples of Hamiltonian stationary Lagrangian tori in CP2[J]. Geom Dedicata, 2006, 118: 173-183.
    [4]
    Mironov A E, Zuo D. On a family of conformally flat Hamiltonian minimal Lagrangian tori in CP3[J]. Int Math Res Not, 2008,2008: 10.1093/imrn/rnn078.
    [5]
    Jiao X X, Wang J. Totally real minimal surfaces in the complex hyperquadrics[J]. Diff Geo Appl, 2013, 31: 540-555.
    [6]
    Hu S, Chen Q, Xu X W. Construction of Lagrangian submanifolds in CPn[J]. Pacific Journal of Math, 2012, 258: 31-49.
    [7]
    Chern S S, Wolfson J. Minimal surfaces by moving frames[J]. Amer J Math, 1983, 105(1):59-83.
    [8]
    Yang K. Complete and Compact Minimal Surface[M]. Dordrecht: Kluwer Academic, 1989.
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