PreprintCC BY 4.0arXiv
Biharmonic Lagrangian surfaces with constant Gaussian curvature in $2$-dimensional complex space forms
Abstract
Constant curvature is one of the most fundamental intrinsic conditions in submanifold geometry. Investigating the existence and classification of biharmonic submanifolds under intrinsic curvature constraints is generally difficult, since the biharmonic equation is expressed in terms of extrinsic data. In this paper, we obtain a complete classification of proper, that is non-minimal, biharmonic Lagrangian surfaces with constant Gaussian curvature in 2-dimensional complex space forms. As a consequence, we classify the proper biharmonic Lagrangian surfaces with flat normal bundle and prove that pseudo-umbilical biharmonic Lagrangian surfaces are necessarily minimal.
Related
- Hamiltonian stationary Lagrangian surfaces of constant Gaussian curvature in complex space forms
- Hamiltonian stationary Lagrangian surfaces in complex space forms with constant-length gradient of the mean curvature
- Four-dimensional pseudo-umbilical biharmonic submanifolds in six-dimensional Riemannian manifolds of constant sectional curvature
- Biharmonic Wintgen ideal submanifolds in Riemannian manifolds of constant sectional curvature
- Hopf type theorem for surfaces of constant weighted mean curvature in Riemannian manifolds
BibTeX
@misc{fu2026biharmonic,
title = {{Biharmonic Lagrangian surfaces with constant Gaussian curvature in $2$-dimensional complex space forms}},
author = {Yu Fu and Yanru Luo and Cezar Oniciuc},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05703},
eprint = {2610.05703},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05703},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Biharmonic Lagrangian surfaces with constant Gaussian curvature in $2$-dimensional complex space forms
AU - Yu Fu
AU - Yanru Luo
AU - Cezar Oniciuc
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.05703
UR - https://arxiv.org/abs/2610.05703
AB - Constant curvature is one of the most fundamental intrinsic conditions in submanifold geometry. Investigating the existence and classification of biharmonic submanifolds under intrinsic curvature constraints is generally difficult, since the biharmonic equation is expressed in terms of extrinsic data. In this paper, we obtain a complete classification of proper, that is non-minimal, biharmonic Lagrangian surfaces with constant Gaussian curvature in 2-dimensional complex space forms. As a consequence, we classify the proper biharmonic Lagrangian surfaces with flat normal bundle and prove that pseudo-umbilical biharmonic Lagrangian surfaces are necessarily minimal.
ER -