Certain 4-manifolds with non-negative sectional curvature
| dc.creator | Cao, Jianguo | |
| dc.date | 2007-01-25 | |
| dc.date | 2007-02-08 | |
| dc.date.accessioned | 2026-07-07T07:45:18Z | |
| dc.date.available | 2026-07-07T07:45:18Z | |
| dc.description | In this paper, we study certain compact 4-manifolds with non-negative sectional curvature $K$. If $s$ is the scalar curvature and $W_+$ is the self-dual part of Weyl tensor, then it will be shown that there is no metric $g$ on $S^2 \times S^2$ with both (i) $K > 0$ and (ii) $ {1/6} s - W_+ \ge 0$. We also investigate other aspects of 4-manifolds with non-negative sectional curvature. One of our results implies a theorem of Hamilton: ``If a simply-connected, closed 4-manifold $M^4$ admits a metric $g$ of non-negative curvature operator, then $M^4$ is one of $S^4$, $\Bbb CP^2$ and $S^2 \times S^2$". Our method is different from Hamilton's and is much simpler. A new version of the second variational formula for minimal surfaces in 4-manifolds is proved. | |
| dc.identifier | https://arxiv.org/abs/math/0701742 | |
| dc.identifier | http://arxiv.org/abs/math/0701742 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123488 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C99, 58C99 | |
| dc.title | Certain 4-manifolds with non-negative sectional curvature | |
| dc.type | text |