Completeness of Lorentz manifolds of constant curvature admitting Killing vector fields (Q688591)

The paper considers Lorentz manifolds with a special structure: of constant curvature \(k\) and/or with a Killing vector field and/or compact \dots A typical result (theorem A, followed by the theorems B--E) reads: if \(k = \) const, \(M\) is compact, and \(M\) admits a timelike Killing vector field, then \(M\) is complete. \(k\leq 0\), and either \(M\) is affinely diffeomorphic to a Euclidean space form (if \(k = 0\)) or some finite covering of \(M\) is a circle bundle (if \(k<0\)). The proofs make use of transformation group methods, of the properly Riemannian metric to a global timelike vector field, and of known classification results for Euclidean or Lorentz spaces of constant curvature.