Transformation groups on complex Stiefel manifolds (Q795387)

The main theorem is: Let \(X=W_{n,k}\) be the complex Stiefel manifold of n-k frames in complex n-space \({\mathbb{C}}^ n\), \(k>n/2\), and let \(G=SU(n)\). Then any nontrivial smooth action of G on X is conjugate to the linear action. The assumptions for this theorem are rather strong, and sophisticated methods in algebraic topology and equivariant cohomology theory are used. Nevertheless the authors promise that this is only the beginning of a general study of large transformation groups on homogeneous spaces.