Homogeneous pregeodesics and the orbits neighbouring a lightlike one

Abstract

The spacelike and timelike orbits of isometric actions on Lorentz manifolds have invariant normal bundles, a fact which permits to study the neighbourhoods of such orbits. As the lightlike orbits do not admit an invariant normal bundle in general, other means are required. It is shown that the concept of homogeneous pregeodesics is helpful in this respect.