Floquet-Bloch functions on non-simply connected manifolds, the Aharonov-Bohm fluxes, and conformal invariants of immersed surfaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909397903474688 |
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| author | Taimanov, I. A. |
| author_facet | Taimanov, I. A. |
| contents | Spectral (Bloch) varieties of multidimensional differential operators on non-simply connected manifolds are defined. In their terms it is given a description of the analytical dependence of the spectra of magnetic Laplacians on non-simply connected manifolds on the values of the Aharonov-Bohm fluxes and a construction of analogues of spectral curves for two-dimensional Dirac operators on Riemann surfaces and, thereby, new conformal invariants of immersions of surfaces into 3- and 4-dimensional Euclidean spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11161 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Floquet-Bloch functions on non-simply connected manifolds, the Aharonov-Bohm fluxes, and conformal invariants of immersed surfaces Taimanov, I. A. Differential Geometry Mathematical Physics Spectral Theory Spectral (Bloch) varieties of multidimensional differential operators on non-simply connected manifolds are defined. In their terms it is given a description of the analytical dependence of the spectra of magnetic Laplacians on non-simply connected manifolds on the values of the Aharonov-Bohm fluxes and a construction of analogues of spectral curves for two-dimensional Dirac operators on Riemann surfaces and, thereby, new conformal invariants of immersions of surfaces into 3- and 4-dimensional Euclidean spaces. |
| title | Floquet-Bloch functions on non-simply connected manifolds, the Aharonov-Bohm fluxes, and conformal invariants of immersed surfaces |
| topic | Differential Geometry Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2403.11161 |