Integral pinched 3-manifolds are space forms

Giovanni Catino, Zindine Djadli

Published 2007-07-03, updated 2007-09-11Version 2

In this paper we prove that, under an explicit integral pinching assumption between the $L^2$-norm of the Ricci curvature and the $L^2$-norm of the scalar curvature, a closed 3-manifold with positive scalar curvature admits an Einstein metric with positive curvature. In particular this implies that the manifold is diffeomorphic to a quotient of ${\Bbb S}^3$.