On compact manifolds with harmonic curvature and positive scalar curvature
Differential Geometry
2016-01-12 v2
Abstract
Let be an -dimensional compact Riemannian manifold with harmonic curvature and positive scalar curvature. Assume that satisfies some integral pinching conditions. We give some rigidity theorems on compact manifolds with harmonic curvature and positive scalar curvature. In particular, Theorem 1.4, Corollary 1.6 and Theorem 1.9 are sharp for our conditions have the additional properties of being sharp. By this we mean that we can precisely characterize the case of equality.
Keywords
Cite
@article{arxiv.1512.00256,
title = {On compact manifolds with harmonic curvature and positive scalar curvature},
author = {Hai-Ping Fu},
journal= {arXiv preprint arXiv:1512.00256},
year = {2016}
}
Comments
arXiv admin note: text overlap with arXiv:1408.0902 by other authors. We revise the old version, and add some content. text overlap with arXiv:1511.07094