Associative Cones and Integrable Systems
| dc.creator | Kong, Shengli | |
| dc.creator | Wang, Erxiao | |
| dc.creator | Terng, Chuu-Lian | |
| dc.date | 2006-02-25 | |
| dc.date.accessioned | 2026-07-07T07:03:46Z | |
| dc.date.available | 2026-07-07T07:03:46Z | |
| dc.description | We identify R^7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit 6-sphere. It is known that a cone over a surface M in S^6 is an associative submanifold of R^7 if and only if M is almost complex in S^6. In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S^6 is the equation for primitive maps associated to the 6-symmetric space G_2/T^2, and use this to explain some of the known results. Moreover, the equation for S^1-symmetric almost complex curves in S^6 is the periodic Toda lattice associated to G_2, and a discussion of periodic solutions is given. | |
| dc.description | to appear in Chinese Annals of Mathematics (2006), a special issue in memory of S. S. Chern | |
| dc.identifier | https://arxiv.org/abs/math/0602565 | |
| dc.identifier | http://arxiv.org/abs/math/0602565 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109101 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C38 | |
| dc.title | Associative Cones and Integrable Systems | |
| dc.type | text |