Harmonic band theory: rigidity of non-zero degree harmonic maps from 2-torus to complex projective space
Abstract
We prove the rigidity of isotropic harmonic maps from a 2-torus to a complex projective space, when they are constructed from holomorphic embeddings associated to complete linear systems. We also prove that this rigidity holds for any holomorphic embeddings without special hyperosculation points, with an extra assumption on the pullbacks of Fubini--Study symplectic forms. These results ensure the rigidity of towers of harmonic bands in condensed matter physics.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Geometric and Algebraic Topology
Publication details
- Journal / source
- Journal of Geometry and Physics
- Volume
- 230
- Pages
- 105969–105969
- Publication date
- 17 August 2026
- Language
- EN