Almost-Einstein manifolds with nonnegative isotropic curvature
[Variétés presque Einstein à courbure isotrope positive ou nulle]
Annales de l'Institut Fourier, Tome 60 (2010) no. 7, pp. 2493-2501.

Soit (M,g), une variété riemannienne compacte simplement connexe de dimension n4, 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 - s n g 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), n4, be a compact simply-connected Riemannian n-manifold with nonnegative isotropic curvature. Given 0<lL, 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 - s n g 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.

DOI : 10.5802/aif.2616
Classification : 53C21
Keywords: Almost-Einstein manifolds, non-negative isotropic curvature
Mot clés : variétés presque-Einstein, courbure isotrope positive ou nulle
Seshadri, Harish 1

1 Indian Institute of Science Department of Mathematics Bangalore 560012 (India)
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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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