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}
}