On the smooth rigidity of almost-Einstein manifolds with nonnegative isotropic curvature

2009/04/05 by Harish Seshadri, Seshadri, Harish
Mathematics · #53C21 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C21

paper · pdf · doi:10.48550/arxiv.0904.0752

5 Pages

arxiv created 2009/04/05 · arxiv updated 2009/12/01

Abstract

Let (Mⁿ,g), n ≥ 4, be a compact simply-connected Riemannian manifold with nonnegative isotropic curvature. Given 0<l≤ L, we prove that there exists \eps = \eps (l,L,n) satisfying the following: If the scalar curvature s of g satisfies l ≤ s ≤ L and the Einstein tensor satisfies | Ric - \frac sng | ≤ \eps then M is diffeomorphic to a symmetric space of compact type. This is a smooth analogue of the result of S. Brendle that a compact Einstein manifold with nonnegative isotropic curvature is isometric to a locally symmetric space.

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