Equations and symmetries of generalized geodesics

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Authors

DOUBROV Boris ŽÁDNÍK Vojtěch

Year of publication 2005
Type Article in Proceedings
Conference Differential geometry and its applications
MU Faculty or unit

Faculty of Education

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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