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@article{555099, author = {Čap, Andreas and Slovák, Jan and Žádník, Vojtěch}, article_location = {Boston}, article_number = {2}, keywords = {parabolic geometries; homogeneous curves; generalized geodesics}, language = {eng}, issn = {1083-4362}, journal = {Transformation Groups}, title = {On distinguished curves in parabolic geometries}, url = {http://www.springerlink.com/content/q0xb50cjh70e59r5/?p=9dc27ea2762b472a9c8ecffaf59dcdbf&pi=2}, volume = {9}, year = {2004} }
TY - JOUR ID - 555099 AU - Čap, Andreas - Slovák, Jan - Žádník, Vojtěch PY - 2004 TI - On distinguished curves in parabolic geometries JF - Transformation Groups VL - 9 IS - 2 SP - 143-166 EP - 143-166 PB - Birkhauser SN - 10834362 KW - parabolic geometries KW - homogeneous curves KW - generalized geodesics UR - http://www.springerlink.com/content/q0xb50cjh70e59r5/?p=9dc27ea2762b472a9c8ecffaf59dcdbf&pi=2 N2 - All parabolic geometries, i.e.~Cartan geometries with homogeneous model a real generalized flag manifold, admit highly interesting classes of distinguished curves. The geodesics of a projective class of connections on a manifold, conformal circles on conformal Riemannian manifolds, and Chern--Moser chains on CR--manifolds of hypersurface type are typical examples. We show that such distinguished curves are always determined by a finite jet in one point, and study the properties of such jets. We also discuss the question when distinguished curves agree up to reparametrization and discuss the distinguished parametrizations in this case. We give a complete description of all distinguished curves for some examples of parabolic geometries. ER -
ČAP, Andreas, Jan SLOVÁK a Vojtěch ŽÁDNÍK. On distinguished curves in parabolic geometries. \textit{Transformation Groups}. Boston: Birkhauser, 2004, roč.~9, č.~2, s.~143-166. ISSN~1083-4362.
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