Curvature and conjugate points in Lorentz symmetric spaces

Abstract

We give some relations between conjugate points and curvature in a locally symmetric Lorentzian manifold. In the compact case, we show that the sectional curvature of timelike planes is non positive, and the lightlike sectional curvature of null planes is non negative. We also compute the lightlike conjugate loci of Cahen-Wallach manifolds, which are an important family of symmetric Lorentzian spaces.