Almost-Einstein manifolds with nonnegative isotropic curvature
Annales de l'Institut Fourier, Volume 60 (2010) no. 7, p. 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 satisfieslsLand the Einstein tensor satisfies Ric -sngεthen 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 satisfaitlsLet que le tenseur d’Einstein satisfait Ric -sngεalors 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.
DOI : https://doi.org/10.5802/aif.2616
Classification:  53C21
Keywords: Almost-Einstein manifolds, non-negative isotropic curvature
@article{AIF_2010__60_7_2493_0,
     author = {Seshadri, Harish},
     title = {Almost-Einstein manifolds with nonnegative isotropic curvature},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {60},
     number = {7},
     year = {2010},
     pages = {2493-2501},
     doi = {10.5802/aif.2616},
     zbl = {1225.53037},
     mrnumber = {2866997},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2010__60_7_2493_0}
}
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/item/AIF_2010__60_7_2493_0/

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