Isospectral potentials and conformally equivalent isospectral metrics on spheres, balls and Lie groups
| dc.creator | Gordon, Carolyn S. | |
| dc.creator | Schueth, Dorothee | |
| dc.date | 2002-09-27 | |
| dc.date | 2002-11-18 | |
| dc.date.accessioned | 2026-07-07T04:51:18Z | |
| dc.date.available | 2026-07-07T04:51:18Z | |
| dc.description | We construct pairs of conformally equivalent isospectral Riemannian metrics $ϕ_1 g$ and $ϕ_2 g$ on spheres $S^n$ and balls $B^{n+1}$ for certain dimensions $n$, the smallest of which is $n=7$, and on certain compact simple Lie groups. In the case of Lie groups, the metric $g$ is left-invariant. In the case of spheres and balls, the metric $g$ is not the standard metric but may be chosen arbitrarily close to the standard one. For the same manifolds $(M,g)$ we also show that the functions $ϕ_1$ and $ϕ_2$ are isospectral potentials for the Schrödinger operator $\hbar^2Δ+ϕ$. To our knowledge, these are the first examples of isospectral potentials and of isospectral conformally equivalent metrics on simply connected closed manifolds. | |
| dc.description | 34 pages, AMS-TeX; revised subsection 5.1 | |
| dc.identifier | https://arxiv.org/abs/math/0209380 | |
| dc.identifier | http://arxiv.org/abs/math/0209380 | |
| dc.identifier | J. Geom. Analysis, Vol. 13, no. 2 (2003), 279 - 306 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65099 | |
| dc.subject | Differential Geometry | |
| dc.subject | Spectral Theory | |
| dc.subject | 58J53; 58J50 | |
| dc.title | Isospectral potentials and conformally equivalent isospectral metrics on spheres, balls and Lie groups | |
| dc.type | text |