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Rigidity of four-dimensional compact manifolds with harmonic Weyl tensor

Differential Geometry 2017-01-10 v2 Geometric Topology

Abstract

The goal of this paper is to investigate the rigidity of 4-dimensional manifolds involving some pinching curvature conditions. To this end, we make use of the approach of biorthogonal curvature which is weaker than the sectional curvature. Here, we prove a rigidity result for 4-dimensional compact manifolds under a suitable lower bound condition on the minimum of the biorthogonal curvature. From this, we improve the pinching constants considered by some preceding works on a rigidity result for 4-dimensional manifolds.

Keywords

Cite

@article{arxiv.1410.3398,
  title  = {Rigidity of four-dimensional compact manifolds with harmonic Weyl tensor},
  author = {Ernani Ribeiro},
  journal= {arXiv preprint arXiv:1410.3398},
  year   = {2017}
}

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Preliminary Version