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Comptes Rendus Mathématique
Volume 341, n° 4
pages 253-258 (août 2005)
Doi : 10.1016/j.crma.2005.06.028
Received : 3 June 2005 ;  accepted : 20 June 2005
Riemannian connections and curvatures on the universal Teichmuller space
Connexions riemanniennes et courbures sur lʼespace de Teichmuller universel
 

Hélène Airault a, b
a INSSET, université de Picardie, 48, rue Raspail, 02100 Saint-Quentin, France 
b Laboratoire CNRS UMR 6140 LAMFA, 33, rue Saint-Leu, 80039 Amiens, France 

Abstract

We define Riemannian connections on the universal Teichmuller space  . For the Levi-Civitaʼs connection on  , the Riemannian curvature tensor is well defined and the Ricci curvature is finite. We obtain several series of infinite dimensional operators which converge. To cite this article: H. Airault, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Résumé

On définit plusieurs connexions riemanniennes sur lʼespace de Teichmuller universel  . Pour la connexion de Levi-Civita sur  , le tenseur de courbure existe et la courbure de Ricci est finie. On obtient plusieurs séries dʼopérateurs de lʼespace de dimension infinie qui convergent. Pour citer cet article : H. Airault, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.


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