TY - JOUR T1 - Existence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds JF - Archiv der Mathematik Y1 - 2020 A1 - Boris Stupovski A1 - Rafael Torres AB -

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.

PB - Springer UR - https://dx.doi.org/10.1007/s00013-020-01511-x ER - TY - JOUR T1 - Topology change and selection rules for high-dimensional spin(1,n)0-Lorentzian cobordisms JF - Transactions of the american mathematical society Y1 - 2020 A1 - Gleb Smirnov A1 - Rafael Torres VL - 373 UR - http://hdl.handle.net/20.500.11767/108858 IS - 3 ER -