Second order variational problem and 2-dimensional concircular geometry

Second order variational problem and 2-dimensional concircular geometry. (English) Zbl 1218.53045

Kubarski, Jan (ed.) et al., Special issue: 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, April 30–May 6, 2007. Luxembourg: University of Luxembourg, Faculty of Science, Technology and Communication (ISBN 978-2-87971-025-9/pbk). Travaux Mathématiques 18, 125-137 (2008).

Summary: 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.

For the entire collection see [Zbl 1168.57001].

MSC:

53C22	Geodesics
53A04	Curves in Euclidean space
58E10	Applications of variational methods to geodesics