In the paper we consider the Stiefel manifold $V_{ n;k}$ as a principal $U(k)$- bundle over the Grassmann manifold and study the cut locus from the unit element. We gave the complete description of this cut locus on $V_{ n;1}$ and presented the sufficient condition on the general case. At the end, we study the complement to the cut locus of $V_{ 2k;k}$.
Categories: math.OC math.DG