Optimal Integral Pinching Results
Differential Geometry
2012-03-05 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1203.0384,
title = {Optimal Integral Pinching Results},
author = {Vincent Bour and Gilles Carron},
journal= {arXiv preprint arXiv:1203.0384},
year = {2012}
}