Abstract
For an isometric action of a Lie group G on a Lorentz manifold (M, g) we consider non-normalizable orbits, i.e. orbits which do not posses a G-invariant normal bundle. Orbits of this type are lightlike. It is shown, that such orbits contain lightlike homogeneous geodesics. Moreover, conditions are given, under which there exists a set of normalizable orbits having an open dense union.
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