Geodesics as products of one‐parameter subgroups in compact lie groups and homogeneous spaces

Abstract

AbstractWe study the geodesic equation for compact Lie groups G and homogeneous spaces , and we prove that the geodesics are orbits of products of one‐parameter subgroups of G, provided that a simple algebraic condition for the Riemannian metric is satisfied. For the group , we relate this type of geodesics to the free motion of a symmetric top. Moreover, by using series of Lie subgroups of G, we construct a wealth of metrics having the aforementioned type of geodesics.