Abstract
Let G be the Lie group of orientation preserving conformal diffeomorphisms of S n . Suppose that the sphere has initially a homogeneous distribution of mass and that the particles are allowed to move only in such a way that two configurations differ in an element of G. There is a Riemannian metric on G, which turns out to be not complete (in particular not invariant), satisfying that a smooth curve in G is a geodesic, if and only if (thought of as a conformal motion) it is force free, i.e., it is a critical point of the kinetic energy functional. We study the force free motions which can be described in terms of the Lie structure of the configuration space.
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