PreprintarXiv licencearXiv
Hamiltonian stationary Lagrangian surfaces of constant Gaussian curvature in complex space forms
Abstract
Let M be a connected Hamiltonian stationary Lagrangian surface of constant Gaussian curvature K in a two-dimensional complex space form Mtilde2(4ε) of constant holomorphic sectional curvature 4ε, and let H denote its mean curvature vector field. We prove that either K=ε or K=0≠ε and |H| is constant. In particular, if |H| is non-constant, then K=ε.
Related
- Hamiltonian stationary Lagrangian surfaces in complex space forms with constant-length gradient of the mean curvature
- Biharmonic Lagrangian surfaces with constant Gaussian curvature in $2$-dimensional complex space forms
- Hamiltonian stationary Lagrangian currents in Ricci-flat Kähler manifolds
- Hopf type theorem for surfaces of constant weighted mean curvature in Riemannian manifolds
- Determinants of Dirichlet and Neumann Laplacians on Constant Curvature Surfaces with Geodesic Polygonal Boundary
BibTeX
@misc{sasahara2026hamiltonian,
title = {{Hamiltonian stationary Lagrangian surfaces of constant Gaussian curvature in complex space forms}},
author = {Toru Sasahara},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16767},
eprint = {2610.16767},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16767},
}
RIS
TY - UNPB
TI - Hamiltonian stationary Lagrangian surfaces of constant Gaussian curvature in complex space forms
AU - Toru Sasahara
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16767
UR - https://arxiv.org/abs/2610.16767
AB - Let M be a connected Hamiltonian stationary Lagrangian surface of constant Gaussian curvature K in a two-dimensional complex space form Mtilde^2(4ε) of constant holomorphic sectional curvature 4ε, and let H denote its mean curvature vector field. We prove that either K=ε or K=0≠ε and |H| is constant. In particular, if |H| is non-constant, then K=ε.
ER -