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Article Dans Une Revue Communications in Analysis and Geometry Année : 2017

A sphere theorem for three dimensional manifolds with integral pinched curvature.

Résumé

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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hal-01059130 , version 1 (29-08-2014)

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Vincent Bour, Gilles Carron. A sphere theorem for three dimensional manifolds with integral pinched curvature.. Communications in Analysis and Geometry, 2017, 25 (1), pp.97-124. ⟨hal-01059130⟩
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