Vol. 296, No. 1, 2018

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ISSN: 0030-8730
Four-manifolds with positive Yamabe constant

Hai-Ping Fu

Vol. 296 (2018), No. 1, 79–104
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
Authors
Hai-Ping Fu
Department of Mathematics
Nanchang University
Nanchang
China