Surfaces isotropes de $\mathbb{O}$ et systèmes intégrables
| dc.creator | Khemar, Idrisse | |
| dc.date | 2005-11-10 | |
| dc.date | 2005-12-05 | |
| dc.date.accessioned | 2026-07-07T06:51:05Z | |
| dc.date.available | 2026-07-07T06:51:05Z | |
| dc.description | We define a notion of isotropic surfaces in $\mathbb{O}$, i.e. on which some canonical symplectic forms vanish. Using the cross-product in $\mathbb{O}$ we define a map $ρ\colon Gr\_2(\mathbb{O})\to S^6$ from the Grassmannian of $\mathbb{O}$ to $S^6$. This allows us to associate to each surface $Σ$ of $\mathbb{O}$ a function $ρ\_Σ\colon Σ\to S^6$. Then we show that the isotropic surfaces in $\mathbb{O}$ such that $ρ\_Σ$ is harmonic are solutions of a completely integrable system. Using loop groups we construct a Weierstrass type representation of these surfaces. By restriction to $ \mathbb{H}\subset\mathbb{O}$ we obtain as a particular case the Hamiltonian Stationary Lagrangian surfaces of $\mathbb{R}^4$, and by restriction to $\text{Im}(\mathbb{H})$ we obtain the CMC surfaces of $\mathbb{R}^3$. | |
| dc.identifier | https://arxiv.org/abs/math/0511258 | |
| dc.identifier | http://arxiv.org/abs/math/0511258 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104867 | |
| dc.subject | Differential Geometry | |
| dc.title | Surfaces isotropes de $\mathbb{O}$ et systèmes intégrables | |
| dc.type | text |