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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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