Hyperkaehler structures on the cotangent bundle of the restricted grassmannian and on a natural complexification of the restricted grassmannian
Tumpach, Alice Barbara
HAL, hal-00022117 / Harvested from HAL
Text on HAL
In this paper, we describe an example of a hyperkaehler quotient of a Banach manifold by a Banach Lie group. Although the initial manifold is not diffeomorphic to a Hilbert manifold (not even to a manifold modelled on a reflexive Banach space), the quotient space obtained is a Hilbert manifold, which can furthermore be identified either with the cotangent space of a connected component of the restricted grassmannian or with a natural complexification of this connected component, thus proving that these two manifolds are isomorphic hyperkaehler manifolds. In addition, Kaehler potentials are computed using Kostant-Souriau's theory of prequantization.
Publié le : 2005-07-05
Classification:  grassmannienne restreinte,  varietes banachiques,  quotients kaehleriens,  quotients hyperkaehlerien,  grassmannienne restreinte.,  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],  [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA],  [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG],  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG],  [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG] 
@article{hal-00022117,
     author = {Tumpach, Alice Barbara},
     title = {Hyperkaehler structures on the cotangent bundle of the restricted grassmannian and on a natural complexification of the restricted grassmannian},
     journal = {HAL},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00022117}
}

Tumpach, Alice Barbara. Hyperkaehler structures on the cotangent bundle of the restricted grassmannian and on a natural complexification of the restricted grassmannian. HAL, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/hal-00022117/