Cut points, conjugate points and Lorentzian comparison theorems

DOI10.1017/S0305004100056188zbMath0528.53050MaRDI QIDQ3310564

John K. Beem, Paul E. Ehrlich

Publication date: 1979

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

globally hyperbolicindex theoryspace-timecut pointsRauch comparison theoremBonnet-Myers diameter theoremindex comparison theoremLorentzian comparison theoremsmaximal geodesics

Mathematics Subject Classification ID

Relativistic cosmology (83F05) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

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Cites Work

• Unnamed Item
• Riemannsche Geometrie im Großen. 2. Aufl
• An application of Morse theory to space-time geometry
• A Morse theory for geodesics on a Lorentz manifold
• Morse theory on timelike and causal curves
• Axioms for indefinite metrics
• Domain of Dependence
• The Large Scale Structure of Space-Time
• Singularities and causality violation

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