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<p>We investigate the geometry of the bitension field of Lagrangian surfaces in complex space forms. We first give a classification of Hamiltonian stationary biminimal Lagrangian surfaces in complex space forms, which allows us to show that Hamiltonian stationary biharmonic Lagrangian surfaces in the complex plane are minimal. Then we investigate the geometry of biminimal or biconservative Lagrangian surfaces in complex space forms. Some classifications of Lagrangian surfaces with constant mean curvature or parallel normalized mean curvature field are obtained.</p>

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Hamiltonian stationary biharmonic Lagrangian surfaces in complex space forms

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • Yanru Luo,
  • Peihan Wang,
  • Xiaoshu Wang

摘要

We investigate the geometry of the bitension field of Lagrangian surfaces in complex space forms. We first give a classification of Hamiltonian stationary biminimal Lagrangian surfaces in complex space forms, which allows us to show that Hamiltonian stationary biharmonic Lagrangian surfaces in the complex plane are minimal. Then we investigate the geometry of biminimal or biconservative Lagrangian surfaces in complex space forms. Some classifications of Lagrangian surfaces with constant mean curvature or parallel normalized mean curvature field are obtained.