Elliptic constructions of hyperkaehler metrics III: Gravitons and Poncelet polygons
| dc.creator | Ionas, Radu A. | |
| dc.date | 2007-12-21 | |
| dc.date.accessioned | 2026-07-07T08:52:25Z | |
| dc.date.available | 2026-07-07T08:52:25Z | |
| dc.description | In the generalized Legendre approach, the equation describing an asymptotically locally Euclidean space of type $D_n$ is found to admit an algebraic formulation in terms of the group law on a Weierstrass cubic. This curve has the structure of a Cayley cubic for a pencil generated by two transversal plane conics, that is, it takes the form $Y^2 = \det ({\cal A}+X{\cal B})$, where ${\cal A}$ and ${\cal B}$ are the defining $3 \times 3$ matrices of the conics. In this light, the equation can be interpreted as the closure condition for an elliptic billiard trajectory tangent to the conic ${\cal B}$ and bouncing into various conics of the pencil determined by the positions of the monopoles. Poncelet's porism guarantees then that once a trajectory closes to a star polygon, any trajectory will close, regardless of the starting point and after the same number of steps. | |
| dc.description | 26 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/0712.3601 | |
| dc.identifier | http://arxiv.org/abs/0712.3601 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145273 | |
| dc.subject | Differential Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Elliptic constructions of hyperkaehler metrics III: Gravitons and Poncelet polygons | |
| dc.type | text |