On the distribution of conjugate points along semi-Riemannian geodesics

Helfer in [6] was the first to produce an example of a spacelike Lorentzian geodesic with a continuum of conjugate points. In this paper we show the following result: given an interval [a,b] of R and any closed subset F of E contained in]a, b], then there exists a Lorentzian manifold (M, g) and a spacelike geodesic 7: [a, b] --> M such that gamma (t) is conjugate to gamma(a) along gamma iff t is an element of F.