Riemannian connections and curvatures on the universal Teichmuller space

Hélène Airault

doi:10.1016/j.crma.2005.06.028

Probability Theory

Riemannian connections and curvatures on the universal Teichmuller space

Presented by: Paul Malliavin

Hélène Airault ^1,²

¹ INSSET, université de Picardie, 48, rue Raspail, 02100 Saint-Quentin, France
² Laboratoire CNRS UMR 6140 LAMFA, 33, rue Saint-Leu, 80039 Amiens, France

Comptes Rendus. Mathématique, Volume 341 (2005) no. 4, pp. 253-258.

Abstract
Résumé

We define Riemannian connections on the universal Teichmuller space $U^{\infty}$ . For the Levi-Civita's connection on $U^{\infty}$ , the Riemannian curvature tensor is well defined and the Ricci curvature is finite. We obtain several series of infinite dimensional operators which converge.

On définit plusieurs connexions riemanniennes sur l'espace de Teichmuller universel $U^{\infty}$ . Pour la connexion de Levi-Civita sur $U^{\infty}$ , le tenseur de courbure existe et la courbure de Ricci est finie. On obtient plusieurs séries d'opérateurs de l'espace de dimension infinie qui convergent.

Received: 2005-06-03
Accepted: 2005-06-20
Published online: 2005-08-03

DOI: 10.1016/j.crma.2005.06.028

Author's affiliations:

Hélène Airault ^{1, 2}

¹ INSSET, université de Picardie, 48, rue Raspail, 02100 Saint-Quentin, France
² Laboratoire CNRS UMR 6140 LAMFA, 33, rue Saint-Leu, 80039 Amiens, France

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     title = {Riemannian connections and curvatures on the universal {Teichmuller} space},
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Hélène Airault. Riemannian connections and curvatures on the universal Teichmuller space. Comptes Rendus. Mathématique, Volume 341 (2005) no. 4, pp. 253-258. doi : 10.1016/j.crma.2005.06.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.06.028/

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