Geometry of curves in parabolic homogeneous spaces
arXiv:1110.0226 · doi:10.1007/s00031-013-9217-x
Abstract
The current paper is devoted to the study of integral curves of constant type in parabolic homogeneous spaces. We construct a canonical moving frame bundle for such curves and give the criterium when it turns out to be a Cartan connection. Generalizations to parametrized curves, to higher-dimensional submanifolds and to general parabolic geometries are discussed.
28 pages; added conditions on the existence of natural symplectic, conformal and G_2 structures on the solution space of a scalar ODE