On the Distribution of Conjugate Points along semi-Riemannian Geodesics

2000/11/06 by Paolo Piccione, Piccione, Paolo, Daniel V. Tausk +1
Mathematics · #34B05 #53C50 #53D25 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:34B05 #msc:53C50 #msc:53D25

paper · pdf · doi:10.48550/arxiv.math/0011038

11 pages, LaTeX2e amsart class

arxiv created 2000/11/06 · arxiv updated 2009/11/30

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]→ M such that γ(t) is conjugate to γ(a) along γ iff t∈ F.

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