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On the Distribution of Conjugate Points along semi-Riemannian Geodesics

Paolo Piccione·Daniel V. Tausk
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Abstract

Helfer in [Pacific J. Math. 164/2 (1994), p. 321--350] 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 $IR$ and any closed subset $F$ of $IR$ contained in $]a,b]$, then there exists a Lorentzian manifold $(M,g)$ and a spacelike geodesic $γ:[a,b]\to M$ such that $γ(t)$ is conjugate to $γ(a)$ along $γ$ iff $t\in F$.

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Paolo Piccione, Daniel V. Tausk. 2000-11-06. On the Distribution of Conjugate Points along semi-Riemannian Geodesics. https://arxiv.org/abs/math/0011038

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