The geometry of partial order on contact transformations of prequantization manifolds
| dc.creator | Simon, Gabi Ben | |
| dc.date | 2006-11-10 | |
| dc.date | 2006-11-11 | |
| dc.date.accessioned | 2026-07-07T07:32:46Z | |
| dc.date.available | 2026-07-07T07:32:46Z | |
| dc.description | In this paper we find connection between the Hofer's metric of the group of Hamiltonian diffeomorphisms of a closed symplectic manifold, with an integral symplectic form, and the geometry, defined in a paper by Eliashberg and Polterovich, of the quantomorphisms group of its prequantization manifold. This gives two main results: First, we calculate, partly, the geometry of the quantomorphisms groups of a prequantization manifolds of an integral symplectic manifold which admits certain Lagrangian foliation. Second, for every prequantization manifold we give a formula for the distance between a point and a distinguished curve in the metric space associated to its group of quantomorphisms. Moreover, our first result is a full computation of the geometry related to the symplectic linear group which can be considered as a subgroup of the contactomorphisms group of suitable prequantization manifolds of the complex projective space. In the course of the proof we use in an essential way the Maslov quasimorphism. | |
| dc.description | 29 pages 2 figures. submitted for publication | |
| dc.identifier | https://arxiv.org/abs/math/0611320 | |
| dc.identifier | http://arxiv.org/abs/math/0611320 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119224 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | 37K65 53D10 53D12 53D50 | |
| dc.title | The geometry of partial order on contact transformations of prequantization manifolds | |
| dc.type | text |