Integral pinched 3-manifolds are space forms

Giovanni Catino; Zindine Djadli

Integral pinched 3-manifolds are space forms

Differential Geometry 2007-09-11 v2 Analysis of PDEs

Authors: Giovanni Catino , Zindine Djadli

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 ${\Bbb S}^3$ .

Keywords

einstein metrics ricci curvature and riemannian geometry riemannian geometry

Cite

@article{arxiv.0707.0338,
  title  = {Integral pinched 3-manifolds are space forms},
  author = {Giovanni Catino and Zindine Djadli},
  journal= {arXiv preprint arXiv:0707.0338},
  year   = {2007}
}

Comments

Some misprints in the first version are corrected

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