Continuous Families of Riemannian manifolds, isospectral on functions but not on 1-forms
| dc.creator | Gornet, Ruth | |
| dc.date | 1997-02-13 | |
| dc.date.accessioned | 2026-07-07T09:12:58Z | |
| dc.date.available | 2026-07-07T09:12:58Z | |
| dc.description | The purpose of this paper is to present the first continuous families of Riemannian manifolds isospectral on functions but not on 1-forms, and simultaneously, the first continuous families of Riemannian manifolds with the same marked length spectrum but not the same 1-form spectrum. The examples presented here are Riemannian three-step nilmanifolds and thus provide a counterexample to the Ouyang-Pesce Conjecture for higher-step nilmanifolds. Ouyang and Pesce independently showed that all isospectral deformations of two-step nilmanifolds must arise from the Gordon-Wilson method for constructing isospectral nilmanifolds. In particular, all continuous families of Riemannian two-step nilmanifolds that are isospectral on functions must also be isospectral on p-forms for all p. They conjectured that all isospectral deformations of nilmanifolds must arise in this manner. These examples arise from a general method for constructing isospectral Riemannian nilmanifolds previously introduced by the author. | |
| dc.description | AMS-TeX, 16 pages | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9702010 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9702010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152207 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58G25, 22E27 (Primary) 53C30, 53C22 (Secondary) | |
| dc.title | Continuous Families of Riemannian manifolds, isospectral on functions but not on 1-forms | |
| dc.type | text |