Second order variational problem and 2-dimensional concircular geometry
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Publication:3396827
zbMATH Open1218.53045arXiv1407.6194MaRDI QIDQ3396827
Publication date: 22 September 2009
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.
Full work available at URL: https://arxiv.org/abs/1407.6194
Geodesics in global differential geometry (53C22) Curves in Euclidean and related spaces (53A04) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)
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