Uniqueness of complex contact structures
| dc.creator | Kebekus, Stefan | |
| dc.date | 2000-04-16 | |
| dc.date | 2000-09-25 | |
| dc.date.accessioned | 2026-07-07T04:34:46Z | |
| dc.date.available | 2026-07-07T04:34:46Z | |
| dc.description | Let X be a complex Fano-manifolds with second Betti-number 1 which carries a contact structure. It follows from previous work that such a manifold can always be covered by lines. Thus, it seems natural to consider the geometry of lines in greater detail. In this brief note we show that if x in X is a general point, then all lines through x are smooth. If X is not the projective space, then the tangent spaces to lines generate the contact distribution at x. As a consequence we obtain that the contact structure on X is unique, a result previously obtained by C. LeBrun in the case that X is a twistor space. | |
| dc.description | reason for resubmission: improved exposition | |
| dc.identifier | https://arxiv.org/abs/math/0004103 | |
| dc.identifier | http://arxiv.org/abs/math/0004103 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59031 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | Primary 53C25, Secondary 14J45, 53C15 | |
| dc.title | Uniqueness of complex contact structures | |
| dc.type | text |