Integral pinched 3-manifolds are space forms

Abstract

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 ${\mathbb{S}}^3$.

Some misprints in the first version are corrected

References in corpus (1)

• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)