1504.00255Apr 1, 2015Final version. To appear in Geom. Ded

Three new almost positively curved manifolds

Jason DeVito

Abstract

A Riemannian manifold is called almost positively curved if the set of points for which all $2$ -planes have positive sectional curvature is open and dense. We find three new examples of almost positively curved manifolds: $Sp(3)/Sp(1)^2$ , and two circle quotients of $Sp(3)/Sp(1)^2$

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. We also show the quasi-positively curved metric of Tapp [26] on

Sp(n+1)/Sp(n-1) Sp(1)

is not almost positively curved if

n\geq 3

.

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Three new almost positively curved manifolds

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