01079nas a2200133   4500008004100000245010500041210006900146260001300215300001000228520061700238100002100855700001900876856005000895       2020                        eng d00aExistence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds0 aExistence of Riemannian metrics with positive biorthogonal curva  bSpringer  a1–93 a<p>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.</p>1 aStupovski, Boris1 aTorres, Rafael  uhttps://dx.doi.org/10.1007/s00013-020-01511-x