Coassociative cones that are ruled by 2-planes
| dc.creator | Fox, Daniel | |
| dc.date | 2005-11-17 | |
| dc.date | 2005-11-21 | |
| dc.date.accessioned | 2026-07-07T06:51:25Z | |
| dc.date.available | 2026-07-07T06:51:25Z | |
| dc.description | It is shown that coassociative cones in R^7 that are r-oriented and ruled by 2-planes are equivalent to CR-holomorphic curves in the oriented Grassmanian of 2-planes in R^7. The geometry of these CR-holomorphic curves is studied and related to holomorphic curves in S^6. This leads to an equivalence between associative cones on one side and the coassociative cones whose second fundamental form has an O(2) symmetry on the other. It also provides a number of methods for explicitly constructing coassociative 4-folds. One method leads to a family of coassociative 4-folds whose members are neither cones nor are ruled by 2-planes. This family directly generalizes the original family of examples provided by Harvey and Lawson when they introduced coassociative geometry. | |
| dc.description | 20 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0511458 | |
| dc.identifier | http://arxiv.org/abs/math/0511458 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104979 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C38 | |
| dc.title | Coassociative cones that are ruled by 2-planes | |
| dc.type | text |