Polysymplectic spaces, s-Kahler manifolds and lagrangian fibrations
| dc.creator | Grassi, Michele | |
| dc.date | 2000-06-21 | |
| dc.date.accessioned | 2026-07-07T04:35:59Z | |
| dc.date.available | 2026-07-07T04:35:59Z | |
| dc.description | In the first part of this paper we begin the study of polysymplectic manifolds, and of their relationship with PDE's. This notion provides a generalization of symplectic manifolds which is very well suited for the geometric study of PDE's with values in a smooth manifold. Some of the standard tools of analytical mechanics, such as the Legendre transformation and Hamilton's equations, are shown to generalize to this new setting. There is a strong link with lagrangian fibrations, which can be used to build polysymplectic manifolds. We then provide the definition and some basic properties of s-Kahler and almost s-Kahler manifolds. These are a generalization of the usual notion of Kahler and almost Kahler manifold, and they reduce to them for s=1. The basic properties of Kahler manifolds, and their Hodge theory, can be generalized to s-Kahler manifolds, with some modifications. The most interesting examples come from semi-flat special lagrangian fibrations of Calabi-Yau manifolds. | |
| dc.description | 56 pages, LaTeX2e, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0006154 | |
| dc.identifier | http://arxiv.org/abs/math/0006154 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59445 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C15 (Primary), 14J32, 17B10, 35A30, 53D12, 70H20 (Secondary) | |
| dc.title | Polysymplectic spaces, s-Kahler manifolds and lagrangian fibrations | |
| dc.type | text |