Harmonic band theory: rigidity of non-zero degree harmonic maps from 2-torus to complex projective space
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908994730196992 |
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| author | Hashimoto, Yoshinori Mera, Bruno Ozawa, Tomoki |
| author_facet | Hashimoto, Yoshinori Mera, Bruno Ozawa, Tomoki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17150 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harmonic band theory: rigidity of non-zero degree harmonic maps from 2-torus to complex projective space Hashimoto, Yoshinori Mera, Bruno Ozawa, Tomoki Mathematical Physics Mesoscale and Nanoscale Physics Algebraic Geometry Differential Geometry 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. |
| title | Harmonic band theory: rigidity of non-zero degree harmonic maps from 2-torus to complex projective space |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2512.17150 |