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Hamiltonian stationary Lagrangian surfaces in complex space forms with constant-length gradient of the mean curvature
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.
Related
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- Determinants of Dirichlet and Neumann Laplacians on Constant Curvature Surfaces with Geodesic Polygonal Boundary
BibTeX
@misc{sasahara2026hamiltonian,
title = {{Hamiltonian stationary Lagrangian surfaces in complex space forms with constant-length gradient of the mean curvature}},
author = {Toru Sasahara},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18508},
eprint = {2609.18508},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18508},
}
RIS
TY - UNPB
TI - Hamiltonian stationary Lagrangian surfaces in complex space forms with constant-length gradient of the mean curvature
AU - Toru Sasahara
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18508
UR - https://arxiv.org/abs/2609.18508
AB - 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.
ER -