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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 and Vojtěch ŽÁDNÍK. On distinguished curves in parabolic geometries. \textit{Transformation Groups}. Boston: Birkhauser, 2004, vol.~9, No~2, p.~143-166. ISSN~1083-4362.
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