New Examples of Obstructions to Non-Negative Sectional Curvatures in Cohomogeneity One Manifolds

K. Grove, L. Verdiani, B. Wilking and W. Ziller gave the first examples of cohomogeneity one manifolds which do not carry invariant metrics with non-negative sectional curvatures. In this paper we generalize their results to a larger family. We also classified all class one representations for a pair (G;H) with G/H some sphere, which are used to construct the examples.