Second order variational problem and 2-dimensional concircular geometry
arXiv:1407.6194
Abstract
It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description is proved. A formal notion of 'spin' force is discovered as a by-product of the variation procedure involving the acceleration.
Proceedings of the 8th Conference on Geometry and Topology of Manifolds (Lie algebroids, dynamical systems and applications) (Luxembourg-Poland-Ukraine conference Przemyśl (Poland)-L'viv (Ukraine), 30.IV.-6.V. 2007). MR2553650(2010i:53065). Several minor typos corrected