Equations and symmetries of generalized geodesics
| Authors | |
|---|---|
| Year of publication | 2005 |
| Type | Article in Proceedings |
| Conference | Differential geometry and its applications |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.karlin.mff.cuni.cz/~dgac/ |
| Field | General mathematics |
| Keywords | Cartan geometry; moving frame; development; differential equations; symmetries |
| Description | We are interested in equations of distinguished curves in general Cartan geometries. In this paper we present a way to construct equations for non-parameterized distinguished curves via symmetry algebras of model curves and Cartan's method of moving frame. We also discuss the correspondence, well-known in particular geometries, between maps preserving generalized geodesics of specific type and morphisms of the geometric structure. As examples we compute equations together with their symmetries for generalized geodesics in projective, projective contact and Lagrangean contact geometries. |
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