Force free conformal motions of the sphere

SALVAI, MARCOS

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS

ELSEVIER SCIENCE BV

Año: 2002 vol. 16 p. 285 - 292

0926-2245

Let G be the Lie group of orientation preserving conformal diffeomor- phisms 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.