International Sophus Lie Centre, Drabstraat 28, 2640 Mortsel, Belgium
We study the conditions when locally homogeneous curves in homogeneous spaces admit a natural projective parameter. In particular, we prove that this is always the case for trajectories of homogeneous nilpotent elements in parabolic spaces. On algebraic level this corresponds to the generalization of Morozov--Jacobson theorem to graded semisimple Lie algebras.
AMSclassification. 17B05, 53C30, 53C40.
Keywords. Homogeneous submanifold, symmetry algebra, nilpotent elements, $sl_2$-tripple.