Harmonic band theory: rigidity of non-zero degree harmonic maps from 2-torus to complex projective space
Mathematical Physics
2026-04-28 v2 Mesoscale and Nanoscale Physics
Algebraic Geometry
Differential Geometry
math.MP
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.
Cite
@article{arxiv.2512.17150,
title = {Harmonic band theory: rigidity of non-zero degree harmonic maps from 2-torus to complex projective space},
author = {Yoshinori Hashimoto and Bruno Mera and Tomoki Ozawa},
journal= {arXiv preprint arXiv:2512.17150},
year = {2026}
}
Comments
16 pages. v2: Corrected an error, resulting in an extra hypothesis on automorphisms in Theorem 1, and other minor changes