We present a unified framework for studying extremal curves on real Stiefel manifolds. We start with a smooth one-parameter family of pseudo-Riemannian metrics on a product of orthogonal groups acting transitively on Stiefel manifolds. We find Euler-Langrange equations for a class of extremal curves that includes geodesics with respect to different Riemannian metrics and smooth curves of constant geodesic curvature. For some specific values of the parameter in the family of pseudo-Riemannian metrics, we recover certain well-known metrics used in applied mathematics.
This is a joint work with K. Hueper (University of Wurzburg, Germany) and F. Silva Leite (University of Coimbra, Portugal)