Cayley 4-form, comass, and triality isomorphisms
| dc.creator | Katz, Mikhail G. | |
| dc.creator | Shnider, Steven | |
| dc.date | 2008-01-01 | |
| dc.date | 2008-10-24 | |
| dc.date.accessioned | 2026-07-07T10:12:33Z | |
| dc.date.available | 2026-07-07T10:12:33Z | |
| dc.description | Following an idea of Dadok, Harvey and Lawson, we apply the triality property of SO(8) to study the comass of certain self-dual 4-forms on R^8. In particular, we prove that the Cayley 4-form has comass 1 and that any self-dual 4-form realizing the maximal Wirtinger ratio is SO(8)-conjugate to the Cayley 4-form. We also use triality to prove that the stabilizer in SO(8) of the Cayley form is Spin(7). The results have applications in systolic geometry, calibrated geometry, and Spin(7) manifolds. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0801.0283 | |
| dc.identifier | http://arxiv.org/abs/0801.0283 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172220 | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 53C23; 17B25 | |
| dc.title | Cayley 4-form, comass, and triality isomorphisms | |
| dc.type | text |