Non-linear Grassmannians as coadjoint orbits
| dc.creator | Haller, Stefan | |
| dc.creator | Vizman, Cornelia | |
| dc.date | 2003-05-06 | |
| dc.date.accessioned | 2026-07-07T04:57:48Z | |
| dc.date.available | 2026-07-07T04:57:48Z | |
| dc.description | For a given manifold $M$ we consider the non-linear Grassmann manifold $Gr_n(M)$ of $n$-dimensional submanifolds in $M$. A closed $(n+2)$-form on $M$ gives rise to a closed 2-form on $Gr_n(M)$. If the original form was integral, the 2-form will be the curvature of a principal $S^1$-bundle over $Gr_n(M)$. Using this $S^1$-bundle one obtains central extensions for certain groups of diffeomorphisms of $M$. We can realize $Gr_{m-2}(M)$ as coadjoint orbits of the extended group of exact volume preserving diffeomorphisms and the symplectic Grassmannians $SGr_{2k}(M)$ as coadjoint orbits in the group of Hamiltonian diffeomorphisms. We also generalize the vortex filament equation as a Hamiltonian equation on $Gr_{m-2}(M)$. | |
| dc.identifier | https://arxiv.org/abs/math/0305089 | |
| dc.identifier | http://arxiv.org/abs/math/0305089 | |
| dc.identifier | Math. Ann. 329(2004), 771--785. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67386 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 58B20 | |
| dc.title | Non-linear Grassmannians as coadjoint orbits | |
| dc.type | text |