Quasi-positive curvature on homogeneous bundles

Abstract

We provide new examples of manifolds which admit a Riemannian metric with sectional curvature nonnegative, and strictly positive at one point. Our examples include the unit tangent bundles of $C{P}^n$, $H{P}^n$ and $Ca{P}^2$, and a family of lens space bundles over $C{P}^n$. All new examples are consequences of a general sufficient condition for a homogeneous fiber bundle over a homogeneous space to admit such a metric.