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Theses

Déformations de métriques Einstein sur des
variétés à singularités coniques

Abstract : Starting with a compact hyperbolic cone-manifold of dimension n>2, we study the deformations of the metric in order to get Einstein cone-manifolds. If the singular locus is a closed codimension 2 submanifold and all cone angles are smaller than 2pi, we show that there is no non-trivial infinitesimal Einstein deformations preserving the cone angles. This result can be interpreted as a higher-dimensional case of the celebrated Hodgson and Kerckhoff's theorem on deformations of hyperbolic 3-cone-manifolds.
If all cone angles are smaller than pi, we also give a construction which associates to any variation of the angles a corresponding infinitesimal Einstein deformation.
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https://tel.archives-ouvertes.fr/tel-00011474
Contributor : Grégoire Montcouquiol <>
Submitted on : Thursday, January 26, 2006 - 6:35:19 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
Long-term archiving on: : Monday, September 17, 2012 - 11:20:43 AM

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  • HAL Id : tel-00011474, version 1

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Grégoire Montcouquiol. Déformations de métriques Einstein sur des
variétés à singularités coniques. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2005. Français. ⟨tel-00011474⟩

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