ON COMPLETENESS OF ORBITS OF KILLING VECTOR-FIELDS

A theorem is proved which reduces the problem of completeness of orbits of Killing vector fields in maximal globally hyperbolic, say, vacuum spacetimes to some properties of the orbits near the Cauchy surface. In particular it is shown that all Killing orbits am complete in maximal developements of asymptotically flat Cauchy data, or of Cauchy data prescribed on a compact manifold.