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Existence of geodesics in static Lorentzian manifolds with convex boundary

Published online by Cambridge University Press:  11 July 2007

P. Piccione
Affiliation:
Instituto de Matemática e Estatística, Departamento de Matemática, Universidade de São Paulo, Brazil ([email protected])

Abstract

We study some global geometric properties of a static Lorentzian manifold Λ embedded in a differentiable manifold M, with possibly non-smooth boundary ∂Λ. We prove a variational principle for geodesics in static manifolds, and using this principle we establish the existence of geodesics that do not touch ∂Λ and that join two fixed points of Λ. The results are obtained under a suitable completeness assumption for Λ that generalizes the property of global hyperbolicity, and a weak convexity assumption on ∂Λ. Moreover, under a non-triviality assumption on the topology of Λ, we also get a multiplicity result for geodesics in Λ joining two fixed points.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2000

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