Optimal Integral Pinching Results

Details Optimal Integral Pinching Results Optimal Integral Pinching Results

2012-03-02

arxiv.org/abs/1203.0384v1

Mathematics

Differential Geometry

Scientific paper

In this article, we generalize the classical Bochner-Weitzenb\"ock theorem for manifolds satisfying an integral pinching on the curvature. We obtain the vanishing of Betti numbers under integral pinching assumptions on the curvature, and characterize the equality case. In particular, we reprove and extend to higher degrees and higher dimensions a number of integral pinching results obtained by M. Gursky for four-dimensional closed manifolds.

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