Four-manifolds with positive Yamabe constant

Hai-Ping Fu

Vol. 296 (2018), No. 1, 79–104

DOI: 10.2140/pjm.2018.296.79

Abstract

We refine a theorem due to Gursky (2000). As applications, we give some rigidity theorems on four-manifolds with positive Yamabe constant. We recover some of Gursky’s results (1998, 2000). We prove some classification theorems of four-manifolds according to some conformal invariants, which reprove and generalize the conformally invariant sphere theorem of Chang, Gursky and Yang (2003).

Keywords

four-manifold, Einstein manifold, harmonic curvature, harmonic Weyl tensor, Yamabe constant

Mathematical Subject Classification 2010

Primary: 53C21

Secondary: 53C20

Milestones

Received: 16 January 2017

Revised: 27 July 2017

Accepted: 5 February 2018

Published: 1 May 2018