English

Hamiltonian stationary Lagrangian surfaces with harmonic mean curvature in complex space forms

Differential Geometry 2026-02-04 v5

Abstract

In this paper, we study Hamiltonian stationary Lagrangian surfaces in complex space forms. We first show that when the mean curvature is a non-zero constant, the second fundamental form is parallel. We then consider the case in which the mean curvature is a non-constant harmonic function. Under the additional assumption that the Gaussian curvature is constant, we obtain a complete classification of such Lagrangian surfaces.

Keywords

Cite

@article{arxiv.2411.11314,
  title  = {Hamiltonian stationary Lagrangian surfaces with harmonic mean curvature in complex space forms},
  author = {Toru Sasahara},
  journal= {arXiv preprint arXiv:2411.11314},
  year   = {2026}
}