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arXiv · 1203.0384

Optimal Integral Pinching Results

Vincent Bour·Gilles Carron
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Abstract

In this article, we generalize the classical Bochner-Weitzenböck 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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Vincent Bour, Gilles Carron. 2012-03-02. Optimal Integral Pinching Results. https://arxiv.org/abs/1203.0384

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