Almost-Einstein manifolds with nonnegative isotropic curvature
[Variétés presque Einstein à courbure isotrope positive ou nulle]
Seshadri, Harish
Annales de l'Institut Fourier, Tome 60 (2010), p. 2493-2501 / Harvested from Numdam
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Soit (M,g), une variété riemannienne compacte simplement connexe de dimension n≥4, à courbure isotrope positive ou nulle. Nous montrons que pour tout 0<l<L, il existe un ε=ε(l,L,n) qui satisfait la propriété suivante : si la courbure scalaire s de g satisfait

l≤s≤L

et que le tenseur d’Einstein satisfait

Ric -sng≤ε

alors M 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 (M,g), n≥4, be a compact simply-connected Riemannian n-manifold with nonnegative isotropic curvature. Given 0<l≤L, we prove that there exists ε=ε(l,L,n) satisfying the following: If the scalar curvature s of g satisfies

l≤s≤L

and the Einstein tensor satisfies

Ric -sng≤ε

then M 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.

Publié le : 2010-01-01
DOI : https://doi.org/10.5802/aif.2616
Classification:  53C21
Mots clés: variétés presque-Einstein, courbure isotrope positive ou nulle 
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     title = {Almost-Einstein manifolds with nonnegative isotropic curvature},
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     year = {2010},
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     doi = {10.5802/aif.2616},
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Seshadri, Harish. Almost-Einstein manifolds with nonnegative isotropic curvature. Annales de l'Institut Fourier, Tome 60 (2010) pp. 2493-2501. doi : 10.5802/aif.2616. http://gdmltest.u-ga.fr/item/AIF_2010__60_7_2493_0/

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