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arXiv · 0707.0338

Integral pinched 3-manifolds are space forms

Giovanni Catino·Zindine Djadli
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Abstract

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 ${\Bbb S}^3$.

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Giovanni Catino, Zindine Djadli. 2007-09-11. Integral pinched 3-manifolds are space forms. https://arxiv.org/abs/0707.0338

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