Abstract
We construct continuous families of nonisometric metrics on simply connected manifolds of dimension n ≥ 9which have the same scattering phase, the same resolvent resonances, and strictly negative sectional curvatures. This situation contrasts sharply with the case of compact manifolds of negative curvature, where Guillemin/Kazhdan, Min-Oo, and Croke/Sharafutdinov showed that there are no nontrivial isospectral deformations of such metrics.
Original language | English |
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Pages (from-to) | 661-677 |
Number of pages | 17 |
Journal | Journal of Geometric Analysis |
Volume | 16 |
Issue number | 4 |
DOIs | |
State | Published - 2006 |
Bibliographical note
Funding Information:Math SubjecCt lassifications5.8 J53, 58J50. Key Wordsa ndP hrases.G eometric scattering, isophasal manifold. Acknowledgemeanntsd Notes. The first author was supported in part by NSF grant DMS-0100829 and DMS-0408419; second author was supported in part by the DFG Priority Programme 1154.
Keywords
- Geometric scattering
- isophasal manifold
ASJC Scopus subject areas
- Geometry and Topology