Four-manifolds with positive Yamabe constant

Hai-Ping Fu
2018 Pacific Journal of Mathematics  
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
more » ... ally invariant sphere theorem of Chang-Gursky-Yang \cite{CGY}.
doi:10.2140/pjm.2018.296.79 fatcat:jhxnmeqp2zaqjbejimkk6hop4u