Positively curved manifolds with symmetry

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Positively curved cohomogeneity one manifolds and 3-Sasakian geometry (2005, methodology): “The first of these is a special case of a more general result in [ Wi3 ], although in our situation it also follows from linear primitivity.”
Examples of Riemannian Manifolds with non-negative sectional curvature (2007, background): “One may view the following theorem as an explanation of why it is so difficult to find new examples [85].”
A Duality Theorem for Riemannian Foliations in Nonnegative Sectional Curvature (2006, methodology): “Using that M/G has no boundary we deduce from Proposition 11.3 in [ Wi ] that any isotropy group of a point p ∈ N is contained in the normalizer N (H )o fH .I n particular it follows that for all p ∈ N the normal space νp(G p ) of the orbit G p is contained in TpN . Therefore for each p ∈ N the dual”
Nonnegatively and Positively curved manifolds (2007, background): “In other words, one can define a pinching family C(s) with C(0) = C by C(s) := la(s),b(s) ( {R ∈ C | Ric ≥ scaln p(s)} ) where the parameters a(s), b(s) defining the linear map la(s),b(s) : S2B(so(n))→ S2B(so(n)) and p(s) are chosen exactly as in [Böhm and Wilking, 2006].”