Four-dimensional manifolds with positive biorthogonal curvature

We classify, up to homeomorphisms, the closed simply-connected $4$-manifolds that admit a Riemannian metric for which averages of pairs of sectional curvatures of orthogonal planes are positive.

Keywords

positive curvature, $4$-manifolds, biorthogonal curvature, scalar curvature, Ricci curvature

2010 Mathematics Subject Classification

53C20, 53C21, 57M50, 57N13, 57R57

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The author was partially supported by the NSF grant DMS-1209387, USA.

Received 28 June 2015

Published 5 July 2017