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.
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.
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@article{CRMATH_2005__341_4_253_0, author = {Airault, H\'el\`ene}, 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}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.06.028/} }
TY - JOUR AU - Airault, Hélène TI - Riemannian connections and curvatures on the universal Teichmuller space JO - Comptes Rendus. Mathématique PY - 2005 SP - 253 EP - 258 VL - 341 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.06.028/ DO - 10.1016/j.crma.2005.06.028 LA - en ID - CRMATH_2005__341_4_253_0 ER -
%0 Journal Article %A Airault, Hélène %T Riemannian connections and curvatures on the universal Teichmuller space %J Comptes Rendus. Mathématique %D 2005 %P 253-258 %V 341 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.06.028/ %R 10.1016/j.crma.2005.06.028 %G en %F CRMATH_2005__341_4_253_0
Airault, Hélène. Riemannian connections and curvatures on the universal Teichmuller space. Comptes Rendus. Mathématique, Tome 341 (2005) no. 4, pp. 253-258. doi : 10.1016/j.crma.2005.06.028. http://archive.numdam.org/articles/10.1016/j.crma.2005.06.028/
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