Integral pinched 3-manifolds are space forms

Details Integral pinched 3-manifolds are space forms Integral pinched 3-manifolds are space forms

2007-07-03

arxiv.org/abs/0707.0338v2

Mathematics

Differential Geometry

Some misprints in the first version are corrected

Scientific paper

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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