Flat Manifolds Isospectral on p-Forms
| dc.creator | Miatello, R. J. | |
| dc.creator | Rossetti, J. P. | |
| dc.date | 2003-03-22 | |
| dc.date.accessioned | 2026-07-07T04:56:16Z | |
| dc.date.available | 2026-07-07T04:56:16Z | |
| dc.description | We study isospectrality on p-forms of compact flat manifolds by using the equivariant spectrum of the Hodge-Laplacian on the torus. We give an explicit formula for the multiplicity of eigenvalues and a criterion for isospectrality. We construct a variety of new isospectral pairs, for instance, pairs of flat manifolds of dimension n=2p, p>1, not homeomorphic to each other, which are isospectral on p-forms but not on q-forms for q different from p. Also, we give manifolds isospectral on p-forms if and only if p is odd, one of them orientable and the other not, and a pair of 0-isospectral flat manifolds, one of them Kahler, and the other not admitting any Kahler structure. We also construct pairs, M, M' of dimension n>5, which are isospectral on functions and such that the Betti numbers of M are less than those of M' for every 0<p<n; and pairs isospectral on p-forms for every p odd, and having different holonomy groups, Z_4 and Z_2+Z_2 respectively. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0303276 | |
| dc.identifier | http://arxiv.org/abs/math/0303276 | |
| dc.identifier | J. Geometric Analysis, vol 11 (2001) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66863 | |
| dc.subject | Differential Geometry | |
| dc.subject | Spectral Theory | |
| dc.subject | 58J53; 20H15 | |
| dc.title | Flat Manifolds Isospectral on p-Forms | |
| dc.type | text |