Integral pinched 3-manifolds are space forms

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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 ${\Bbb S}^3$.
Some misprints in the first version are corrected

Keywords

Differential Geometry, Analysis of PDEs, 53C24; 53C20; 53C21; 53C25

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/137580

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0707.0338
 http://arxiv.org/abs/0707.0338

Collections

arXiv