Using the recent work of Bettiol, we show that a first-order conformal deformation of Wilking’s metric of almost-positive sectional curvature on $S2\times S3$ yields a family of metrics with strictly positive average of sectional curvatures of any pair of 2-planes that are separated by a minimal distance in the 2-Grassmanian. A result of Smale allows us to conclude that every closed simply connected 5-manifold with torsion-free homology and trivial second Stiefel–Whitney class admits a Riemannian metric with a strictly positive average of sectional curvatures of any pair of orthogonal 2-planes.

%B Archiv der Mathematik %I Springer %P 1–9 %G eng %U https://dx.doi.org/10.1007/s00013-020-01511-x %R 10.1007/s00013-020-01511-x %0 Journal Article %J Transactions of the american mathematical society %D 2020 %T Topology change and selection rules for high-dimensional spin(1,n)0-Lorentzian cobordisms %A Gleb Smirnov %A Rafael Torres %B Transactions of the american mathematical society %V 373 %P 1731-1747 %G eng %U http://hdl.handle.net/20.500.11767/108858 %N 3 %9 Journal article %& 1731 %R 10.1090/tran/7939