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

TitleExistence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds
Publication TypeJournal Article
Year of Publication2020
AuthorsStupovski, B, Torres, R
JournalArchiv der Mathematik
Pagination1–9
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 $S2\times S3$ 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.

URLhttps://dx.doi.org/10.1007/s00013-020-01511-x
DOI10.1007/s00013-020-01511-x

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