Force free conformal motions of the sphere.
The author studies force free motion of a nonrigid body on the \(n\)-sphere, equipped with its standard metric. Nonrigidness is described by the fact that two configurations differ by the action of an element of the conformal group \(G\) of the sphere. Following the methods described by \textit{V. I. Arnold} in ``Mathematical Methods of Classical Mechanics'', Springer, New York (1978; Zbl 0386.70001), the author associates to a distribution of mass on the sphere a Riemanniann metric on \(G\) in such a way that geodesics on \(G\) induce force free motions of the mass. He then gives properties of this metric. In particular \(G\) is not complete with respect to it.
scientific article; zbMATH DE number 1780876
scientific article