The Introduction of Boehner's Technique on Lorentzian Manifolds

Bochner's technique is applied to the study of timelike vectors fields on a Lorentzian manifold. In the compact case, a Lorentzian Bochner integral formula is obtained. As a consequence, compact Ricci flat Lorentzian manifolds admitting a timelike conformal vector field are classified. Both in the compact and non compact case, some obstructions to the existence of certain types of timelike vector fields are given