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

Toru Sasahara

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arXiv · 2411.11314

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

Toru Sasahara

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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.

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BibTeX RIS

Toru Sasahara. 2024-11-18. Hamiltonian stationary Lagrangian surfaces with harmonic mean curvature in complex space forms. https://arxiv.org/abs/2411.11314

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