Rigidity of non-negatively curved metrics on open five-dimensional manifolds
| dc.creator | Marenich, Valery | |
| dc.date | 2004-11-29 | |
| dc.date.accessioned | 2026-07-07T05:14:47Z | |
| dc.date.available | 2026-07-07T05:14:47Z | |
| dc.description | As the first step in the direction of the Hopf conjecture on the non-existence of metrics with positive sectional curvature on $S^2 \times S^2$ D.Gromoll and K.Tapp in [GT] suggested the following (Weak Hopf) conjecture (on the rigidity of non-negatively curved metrics on $S^2 \times R^3$): "The boundary $S^2\times S^2$ of the $S^2 \times B^3\subset S^2 \times R^3$ with an arbitrary complete metric of non-negative sectional curvature contains a point where a curvature of $S^2 \times S^2$ vanish". In this note we verify this. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0411632 | |
| dc.identifier | http://arxiv.org/abs/math/0411632 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73413 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C20; 53C21 | |
| dc.title | Rigidity of non-negatively curved metrics on open five-dimensional manifolds | |
| dc.type | text |