Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Cap, A., Slovák, J. & Zádník, V. On Distinguished Curves in Parabolic Geometries. Transformation Groups 9, 143–166 (2004). https://doi.org/10.1007/s00031-004-7009-z
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s00031-004-7009-z