Isospectral CR manifolds with respect to the Kohn Laplacian
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908407399710720 |
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| author | Gutierrez, Gerson Lauret, Emilio A. Rossetti, Juan Pablo |
| author_facet | Gutierrez, Gerson Lauret, Emilio A. Rossetti, Juan Pablo |
| contents | We prove that the spectrum of the Kohn Laplacian does not determine the equivalence classes of CR manifolds. We construct pairs of odd-dimensional elliptic manifolds that are not equivalent as CR manifolds but whose Kohn Laplacians have the same spectrum. These manifolds are endowed with the CR structures inherited from the canonical CR structure on the sphere of the same dimension. We provide three different constructions among lens spaces and an additional one among elliptic manifolds with non-cyclic fundamental groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15214 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Isospectral CR manifolds with respect to the Kohn Laplacian Gutierrez, Gerson Lauret, Emilio A. Rossetti, Juan Pablo Differential Geometry Complex Variables Spectral Theory 58J53 (Primary), 32V05, 32V20 (Secondary) We prove that the spectrum of the Kohn Laplacian does not determine the equivalence classes of CR manifolds. We construct pairs of odd-dimensional elliptic manifolds that are not equivalent as CR manifolds but whose Kohn Laplacians have the same spectrum. These manifolds are endowed with the CR structures inherited from the canonical CR structure on the sphere of the same dimension. We provide three different constructions among lens spaces and an additional one among elliptic manifolds with non-cyclic fundamental groups. |
| title | Isospectral CR manifolds with respect to the Kohn Laplacian |
| topic | Differential Geometry Complex Variables Spectral Theory 58J53 (Primary), 32V05, 32V20 (Secondary) |
| url | https://arxiv.org/abs/2312.15214 |