On Closed Six-Manifolds Admitting Metrics with Positive Sectional Curvature and Non-Abelian Symmetry

We study the topology of closed, simply-connected, 6-dimensional Riemannian manifolds
of positive sectional curvature which admit isometric actions by SU(2) or SO(3). We show that their
Euler characteristic agrees with that of the known examples, i.e., S6, CP3, the Wallach space SU(3)/T 2 and the biquotient SU(3)//T 2. We also classify, up to equivariant diffeomorphism, certain actions
without exceptional orbits and show that there are strong restrictions on the exceptional strata.