Remarks on global geodesic properties of G\"odel type spacetimes
  The aim of this paper is to review and complete the study of geodesics on G\"odel type spacetimes initiated in [8] and improved in [2] of the References. In particular, we prove some new results on geodesic connectedness and geodesic completeness for these spacetimes. 
Rossella Bartolo, Anna Maria Candela, Jos\'e Luis Flores
math.DG