Inhomogeneous spaces of positive curvature

Abstract

We describe the geometry and the topology of a compact simply connected positively curved Riemannian 6-manifold F′ which is related to the flag manifold F over C P 2, and an infinite series of simply connected circle bundles over F′, also with positive sectional curvature. All of these spaces are biquotients of the Lie group SU (3) and they are not homeomorphic to a homogeneous space of positive curvature.