Force free conformal motions of the sphere

✍ Scribed by Marcos Salvai

• Book ID: 104358150
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 89 KB
• Volume: 16
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(02)00061-x

✦ Synopsis

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.