Hamiltonian stationary Lagrangian surfaces in complex space forms with constant-length gradient of the mean curvature
Year: 2026
Type: preprint
Abstract: We study Hamiltonian stationary Lagrangian surfaces in complex space forms with nowhere-zero mean curvature vector $H$. We prove that if the Gaussian curvature is constant and $\grad|H|$ has positive constant length, then both the surface and the ambient space are flat. Moreover, the immersion is locally congruent to the known surface obtained as the product of a Cornu spiral and its reflection.
Source: arXiv (Cornell University)
Author: Sasahara, Toru
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213514630