Soit , une variété riemannienne compacte simplement connexe de dimension , à courbure isotrope positive ou nulle. Nous montrons que pour tout , il existe un qui satisfait la propriété suivante : si la courbure scalaire de satisfait
et que le tenseur d’Einstein satisfait
alors est difféomorphe à un espace symétrique de type compact.
Ceci est lié au résultat de S. Brendle sur la rigidité métrique des variétés d’Einstein à courbure isotrope positive ou nulle.
Let , , be a compact simply-connected Riemannian -manifold with nonnegative isotropic curvature. Given , we prove that there exists satisfying the following: If the scalar curvature of satisfies
and the Einstein tensor satisfies
then is diffeomorphic to a symmetric space of compact type.
This is related to the result of S. Brendle on the metric rigidity of Einstein manifolds with nonnegative isotropic curvature.
Keywords: Almost-Einstein manifolds, non-negative isotropic curvature
Mot clés : variétés presque-Einstein, courbure isotrope positive ou nulle
@article{AIF_2010__60_7_2493_0, author = {Seshadri, Harish}, title = {Almost-Einstein manifolds with nonnegative isotropic curvature}, journal = {Annales de l'Institut Fourier}, pages = {2493--2501}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {7}, year = {2010}, doi = {10.5802/aif.2616}, zbl = {1225.53037}, mrnumber = {2866997}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2616/} }
TY - JOUR AU - Seshadri, Harish TI - Almost-Einstein manifolds with nonnegative isotropic curvature JO - Annales de l'Institut Fourier PY - 2010 SP - 2493 EP - 2501 VL - 60 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2616/ DO - 10.5802/aif.2616 LA - en ID - AIF_2010__60_7_2493_0 ER -
%0 Journal Article %A Seshadri, Harish %T Almost-Einstein manifolds with nonnegative isotropic curvature %J Annales de l'Institut Fourier %D 2010 %P 2493-2501 %V 60 %N 7 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2616/ %R 10.5802/aif.2616 %G en %F AIF_2010__60_7_2493_0
Seshadri, Harish. Almost-Einstein manifolds with nonnegative isotropic curvature. Annales de l'Institut Fourier, Tome 60 (2010) no. 7, pp. 2493-2501. doi : 10.5802/aif.2616. http://www.numdam.org/articles/10.5802/aif.2616/
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