Four manifolds with postive Yamabe constant
Differential Geometry
2018-05-23 v5
Abstract
We refine Theorem A due to Gursky \cite{G3}. As applications, we give some rigidity theorems on four-manifolds with postive Yamabe constant. In particular, these rigidity theorems 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. We prove some classification theorems of four manifolds according to some conformal invariants (see Theorems 1.3 and 1.6), which generalize the conformally invariant sphere theorem of Chang-Gursky-Yang \cite{CGY}.
Cite
@article{arxiv.1601.04796,
title = {Four manifolds with postive Yamabe constant},
author = {Hai-Ping Fu},
journal= {arXiv preprint arXiv:1601.04796},
year = {2018}
}
Comments
This article whose number is arXiv:1601.04796 had been withdrawn since it need been modified to give correct and full citations of previous work. Now I revise it