Cohomogeneity and positive curvature in low dimensions
The classification of compact positively curved Riemannian manifolds (CPCM's) is a basic problem. A compact, connected Lie group \(G\) is said to act by cohomogeneity \(k\) on a Riemannian manifold if \(G\) acts effectively and isometrically with a principal orbit of codimension \(k\). The main result of the paper is the following: if \(M^ n\), \(2\leq n\leq 6\), is a simply connected CPCM admitting a cohomogeneity one action with respect to this metric, then \(M^ n\) is diffeomorphic to either \(S^ n\) or \(CP^{n/2}\).
scientific article; zbMATH DE number 567456