Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 47, Issue 5, Pages 3085-3102Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0362-546X(01)00427-8
Keywords
Riemannian; Lorentzian and affine manifolds; geodesic connectedness; convex boundary; pseudoconvexity; space of geodesics; Lorentzian and affine torus; spaceform; variational methods; critical points; Ljusternik-Schnirelman theory; stationary and splitting manifolds; multiwarped and Generalized Robertson; Walker spacetimes; Brower's topological degree
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The results and techniques about the geodesic connectedness of semi-Riemannian manifolds are reviewed. For the Riemannian case, this imply discussions on the Cauchy boundary. For the Lorentzian case, the results are not so general, but Avery different techniques cover many particular cases: spaceforms, disprisoning and pseudoconvex manifolds, stationary, globally hyperbolic or multiwarped spacetimes. Some of them are applicable to semi-Riemannian manifolds with higher index or even to manifolds with just an affine connection.
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