Timeline for General questions on the eigenfunctions of Laplacian and Dirac operators
Current License: CC BY-SA 3.0
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| Sep 19, 2021 at 10:26 | comment | added | emiliocba | In Remark 6.4 of arxiv.org/abs/1412.2599v1, Sebastian Boldt and I gave examples of Dirac-isospectral but not Hodge-Laplace isospectral lens spaces. | |
| Jun 4, 2017 at 10:45 | comment | added | Bernd Ammann | For the Laplace-Beltrami operator the answer is given in Theorem 5.6 in link. There are manifolds isospectral for the Laplace-Beltrami, but not for the Dirac operator. One can also construct manifolds which are isospectral for the Hodge-Laplacian, but not for the Dirac operator by changing the spin structure, this works even on tori. I expect that examples isospectral for the Hodge-Laplacian, but non-Dirac-isospectral for any choice of spin structure should exist, but I do not think that anyone has constructed such pairs so far. | |
| Jun 2, 2017 at 9:40 | comment | added | Z. Ye | Nice answer! I still want to know if Dirac operator gives a bit more information. From your answer it's pretty clear that the Dirac operator can distinguish different spin structures. But for a trivial spin structure, it seems that the spectrum of Dirac operator will not give more information than Laplaician? Thank you very much. | |
| May 19, 2017 at 11:43 | review | First posts | |||
| May 19, 2017 at 11:44 | |||||
| May 19, 2017 at 11:41 | history | answered | Bernd Ammann | CC BY-SA 3.0 |