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@inproceedings{610744, author = {Doubrov, Boris and Žádník, Vojtěch}, address = {Praha}, booktitle = {Differential geometry and its applications}, keywords = {Cartan geometry; moving frame; development; differential equations; symmetries}, language = {eng}, location = {Praha}, isbn = {80-86732-63-0}, pages = {203-216}, publisher = {Matfyzpress}, title = {Equations and symmetries of generalized geodesics}, url = {http://www.karlin.mff.cuni.cz/~dgac/}, year = {2005} }
TY - JOUR ID - 610744 AU - Doubrov, Boris - Žádník, Vojtěch PY - 2005 TI - Equations and symmetries of generalized geodesics PB - Matfyzpress CY - Praha SN - 8086732630 KW - Cartan geometry KW - moving frame KW - development KW - differential equations KW - symmetries UR - http://www.karlin.mff.cuni.cz/~dgac/ N2 - 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. ER -
DOUBROV, Boris a Vojtěch ŽÁDNÍK. Equations and symmetries of generalized geodesics. In \textit{Differential geometry and its applications}. Praha: Matfyzpress, 2005, s.~203-216, 13 s. ISBN~80-86732-63-0.
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