Bochner’s technique on Lorentzian manifolds and infinitesimal conformal symmetries

Alfonso Romero and Miguel Sánchez

Vol. 186 (1998), No. 1, 141–148

DOI: 10.2140/pjm.1998.186.141

Abstract

Bochner’s technique is applied to the study of timelike vector fields on a Lorentzian manifold. A Lorentzian Bochner integral formula is obtained; as a consequence, compact Ricci-flat Lorentzian manifolds admitting a timelike conformal vector field are classified. Some obstructions to the existence of timelike conformal vector fields and other conformal symmetries are also given.

Milestones

Received: 24 April 1997

Revised: 29 September 1997

Published: 1 November 1998