On the Weyl tensor of a self-dual complex 4-manifold
| dc.creator | Belgun, F. A. | |
| dc.date | 2000-02-04 | |
| dc.date.accessioned | 2026-07-07T04:33:35Z | |
| dc.date.available | 2026-07-07T04:33:35Z | |
| dc.description | We study complex 4-manifolds with holomorphic self-dual conformal structures, and we obtain an interpretation of the Weyl tensor of such a manifold as the projective curvature of a field of cones on the ambitwistor space. In particular, its vanishing is implied by the existence of some compact, simply-connected, null-geodesics. We also relate the Cotton-York tensor of an umbilic hypersurface to the Weyl tensor of the ambient. As a consequence, a conformal 3-manifold or a self-dual 4-manifold admitting a rational curve as a null-geodesic is conformally flat. We show that the projective structure of the beta-surfaces of a self-dual manifold is flat. | |
| dc.description | 42 pages, 18 figures | |
| dc.identifier | https://arxiv.org/abs/math/0002029 | |
| dc.identifier | http://arxiv.org/abs/math/0002029 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58627 | |
| dc.subject | Differential Geometry | |
| dc.title | On the Weyl tensor of a self-dual complex 4-manifold | |
| dc.type | text |