Geodesic
Projective reparametrization of homogeneous curves
Archivum mathematicum, Tome 41 (2005) no. 1, pp. 129-133 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 17B20, 17B70, 53C30
Keywords: homogeneous submanifold; symmetry algebra; nilpotent elements; $sl_2$-tripple 
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Doubrov, Boris. Projective reparametrization of homogeneous curves. Archivum mathematicum, Tome 41 (2005) no. 1, pp. 129-133. http://geodesic.mathdoc.fr/item/ARM_2005_41_1_a11/

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