Address.
International Sophus Lie Centre,
Drabstraat 28, 2640 Mortsel, Belgium
E-mail. doubrov@islc.org
Abstract.
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.