On the distribution of conjugate points along semi-Riemannian geodesies
نویسندگان
چکیده
منابع مشابه
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 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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15 صفحه اولOn the Topology of Riemannian Manifolds Where the Conjugate Points Have a Similar Distribution as in Symmetric Spaces of Rank 1 by Wilhelm Klingenberg
1. Manifolds similar to spheres. 1.1. Let S=S be the w-dimensional sphere, endowed with the usual metric of constant Riemannian curvature 1. Let G=(p(s)), 0^s< oo, be a geodesic ray in S, s being the arc length. Then the conjugate points of £(0) on G occur at S = IT, I a positive integer, with multiplicity n — 1. Let G be a geodesic ray in a Riemannian manifold M=M of dimension n. The following...
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2003
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2003.v11.n1.a3