Comparison and Rigidity Theorems in Semi-Riemannian Geometry
| dc.creator | Andersson, L. | |
| dc.creator | Howard, R. | |
| dc.date | 1997-07-25 | |
| dc.date.accessioned | 2026-07-07T09:13:16Z | |
| dc.date.available | 2026-07-07T09:13:16Z | |
| dc.description | The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian case correspond to one-sided bounds on the sectional curvatures. Starting from 2-dimensional rigidity results and using an inductive technique, a new class of gap-type rigidity theorems is proved for semi-Riemannian manifolds of arbitrary index, generalizing those first given by Gromov and Greene-Wu. As applications we prove rigidity results for semi-Riemannian manifolds with simply connected ends of constant curvature. | |
| dc.description | 46 pages, amsart, to appear in Comm. Anal. Geom | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9707020 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9707020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152266 | |
| dc.subject | Differential Geometry | |
| dc.title | Comparison and Rigidity Theorems in Semi-Riemannian Geometry | |
| dc.type | text |