Almost-Einstein manifolds with nonnegative isotropic curvature
Annales de l'Institut Fourier, Volume 60 (2010) no. 7, pp. 2493-2501.

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

lsL

and the Einstein tensor satisfies

Ric -sngε

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.

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

lsL

et que le tenseur d’Einstein satisfait

Ric -sngε

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.

Received:
Accepted:
DOI: 10.5802/aif.2616
Classification: 53C21
Keywords: Almost-Einstein manifolds, non-negative isotropic curvature
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, Volume 60 (2010) no. 7, pp. 2493-2501. doi : 10.5802/aif.2616. https://aif.centre-mersenne.org/articles/10.5802/aif.2616/

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