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×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.

Existence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds / Stupovski, Boris; Torres, Rafael. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - 115:5(2020), pp. 589-597. [10.1007/s00013-020-01511-x]

Existence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds

Stupovski, Boris;Torres, Rafael
2020-01-01

Abstract

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×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.
2020
115
5
589
597
Stupovski, Boris; Torres, Rafael
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/114489
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