  In this paper, we classify compact simply connected cohomogeneity one
manifolds up to equivariant diffeomorphism whose isotropy representation by the
connected component of the principal isotropy subgroup has three or less
irreducible summands. The manifold is either a bundle over a homogeneous space
or an irreducible symmetric space. As a corollary such manifolds admit an
invariant metric with non-negative sectional curvature.
