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}
}
Comments
Preliminary Version