A sphere theorem for three dimensional manifolds with integral pinched curvature

2014/08/29 by Vincent Bour, Bour, Vincent, Gilles Carron +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1408.7091

arxiv created 2014/08/29 · arxiv updated 2014/09/01

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.

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• Connected sum of manifolds with spectral Ricci lower bounds

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