A sphere theorem for three dimensional manifolds with integral pinched curvature

A sphere theorem for three dimensional manifolds with integral pinched curvature

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 classific...

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Veröffentlicht in:Communications in analysis and geometry 2017, Vol.25 (1), p.97-124
Hauptverfasser: Bour, Vincent, Carron, Gilles
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Differential Geometry
Mathematics
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description 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.
doi_str_mv 10.4310/CAG.2017.v25.n1.a3
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Mathematics
title A sphere theorem for three dimensional manifolds with integral pinched curvature
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