A sphere theorem for three dimensional manifolds with integral pinched curvature
Differential Geometry
2014-09-01 v1
Abstract
In a previous paper, we proved a number of optimal rigidity results for Riemannian manifolds of dimension greater than four whose curvature satisfy an integral pinching. In this article, we use the same integral Bochner technique to extend the results in dimension three. Then, by using the classification of closed three-manifolds with nonnegative scalar curvature and a few topological considerations, we deduce optimal sphere theorems for three-dimensional manifolds with integral pinched curvature.
Keywords
Cite
@article{arxiv.1408.7091,
title = {A sphere theorem for three dimensional manifolds with integral pinched curvature},
author = {Vincent Bour and Gilles Carron},
journal= {arXiv preprint arXiv:1408.7091},
year = {2014}
}