We define Riemannian connections on the universal Teichmuller space . For the Levi-Civita's 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.
On définit plusieurs connexions riemanniennes sur l'espace 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 d'opérateurs de l'espace de dimension infinie qui convergent.
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Hélène Airault 1, 2
@article{CRMATH_2005__341_4_253_0, author = {H\'el\`ene Airault}, title = {Riemannian connections and curvatures on the universal {Teichmuller} space}, journal = {Comptes Rendus. Math\'ematique}, pages = {253--258}, publisher = {Elsevier}, volume = {341}, number = {4}, year = {2005}, doi = {10.1016/j.crma.2005.06.028}, language = {en}, }
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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