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Varietes kaehleriennes et hyperkaeleriennes de dimension infinie

Abstract : In the first chapter of this thesis, 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 be furthermore identified either with the cotangent space of a connected component of the restricted Grassmannian or with a natural complexification of this connected component.

The second chapter is divided into 3 parts. The first part is devoted to a classification Theorem of irreducible Hermitien-symmetric affine coadjoint orbits of L*-groups of compact type. In the second part, we give a proof of Mostow's Decomposition Theorem for a semi-simple L*-group. In the last part, we construct an hyperkaehler structure on complexifications of Hermitian-symmetric affine coadjoint orbits of semi-simple L*-group of compact type.
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Contributor : Alice Barbara Tumpach <>
Submitted on : Wednesday, March 22, 2006 - 5:02:56 PM
Last modification on : Thursday, March 5, 2020 - 6:26:58 PM
Long-term archiving on: : Saturday, April 3, 2010 - 10:01:23 PM


  • HAL Id : tel-00012012, version 1



Alice Barbara Tumpach. Varietes kaehleriennes et hyperkaeleriennes de dimension infinie. Mathématiques [math]. Ecole Polytechnique X, 2005. Français. ⟨tel-00012012⟩



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