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We study the topology of closed, simply-connected, 6-dimensional Riemannianmanifolds of positive sectional curvature which admit isometric actions by$SU(2)$ or $SO(3)$. We show that their Euler characteristic agrees with that ofthe known examples, i.e. $S^6$, $\mathbb{CP}^3$, the Wallach space $SU(3)/T^2$and the biquotient $SU(3)//T^2$. We also classify, up to equivariantdiffeomorphism, certain actions without exceptional orbits and show that thereare strong restrictions on the exceptional strata.

On Closed 6-Manifolds Admitting Riemannian Metrics with Positive Sectional Curvature and Non-Abelian Symmetry