Cohomogeneity One Manifolds of Even Dimension with Strictly Positive Sectional Curvature

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Examples of Riemannian Manifolds with non-negative sectional curvature (2007, background): “Verdiani [80] classified all positively curved cohomogeneity one manifolds.”
Positively curved manifolds with symmetry (2006, background): “Verdiani [19] has shown that an even dimensional simply connected positively curved cohomogeneity one manifold is diffeomorphic to a rank one symmetric space.”
Nonnegatively and Positively curved manifolds (2007, background): “In fact Walschap [1988] showed that given an open four manifold with a soul S(2) for which any zero curvature plane is tangent to one of the Perelman flats from Theorem 3.”
Positively curved cohomogeneity one manifolds and 3-Sasakian geometry (2005, background): “One easily sees that if an action of G on a sphere in R n is not essential, and no normal subaction is essential, then G = L1L2 and R n = V1 ⊕ V2 such that G preserves Vi”