Geometry of curves in parabolic homogeneous spaces
Differential Geometry
2013-07-02 v2
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.
Keywords
Cite
@article{arxiv.1110.0226,
title = {Geometry of curves in parabolic homogeneous spaces},
author = {Boris Doubrov and Igor Zelenko},
journal= {arXiv preprint arXiv:1110.0226},
year = {2013}
}
Comments
28 pages; added conditions on the existence of natural symplectic, conformal and G_2 structures on the solution space of a scalar ODE