ALMOST-EINSTEIN MANIFOLDS WITH NONNEGATIVE ISOTROPIC CURVATURE

作者：Seshadri Harish^*

来源：Annales de l'Institut Fourier, 2010, 60(7): 2493-2501.

DOI：10.5802/aif.2616

• Almost-Einstein manifolds
• non-negative isotropic curvature

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 epsilon = epsilon(l, L, n) satisfying the following: If the scalar curvature s of g satisfies
l <= s <= L
and the Einstein tensor satisfies
vertical bar Ric - s/n g vertical bar <= epsilon
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.

• 出版日期2010