Asian Journal of Mathematics

Volume 21 (2017)

Number 2

Four-dimensional manifolds with positive biorthogonal curvature

Pages: 391 – 396



Renato G. Bettiol (Department of Mathematics,University of Pennsylvania, Philadelphia, Penn., U.S.A.)


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.


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

2010 Mathematics Subject Classification

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

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

Received 28 June 2015

Published 5 July 2017