Geometry of curves in parabolic homogeneous spaces

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

References in corpus (3)

• On local geometry of rank 3 distributions with 6-dimensional square
• Prolongation of quasi-principal frame bundles and geometry of flag structures on manifolds
• Symmetries of trivial systems of ODEs of mixed order

Cited by in corpus (8)

• Prolongation of quasi-principal frame bundles and geometry of flag structures on manifolds
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• The dancing metric, ${\mathrm{G}}_2$-symmetry and projective rolling
• Geometry of Fanning Curves in Divisible Grassmannians
• Geometry of rank 2 distributions with nonzero Wilczynski invariants and affine control systems with one input
• Toda field theories and integral curves of standard differential systems
• Extrinsic Geometry and Linear Differential Equations
• Vector distributions with very large symmetries via rational normal curves