Some connections between global hyperbolicity and geodesic completeness

DOI10.1016/0393-0440(89)90004-1zbMath0677.53071OpenAlexW1976956830MaRDI QIDQ1123428

Gregory J. Galloway

Publication date: 1989

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(89)90004-1

zbMATH Keywords

global hyperbolicitygeodesic completenessstrong energy conditioncausally completesectional curvature condition

Mathematics Subject Classification ID

Applications of global differential geometry to the sciences (53C80) Space-time singularities, cosmic censorship, etc. (83C75) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (7)

Geometry of weighted Lorentz–Finsler manifolds II: A splitting theorem ⋮ A note on null distance and causality encoding ^* ⋮ Achronal limits, Lorentzian spheres, and splitting ⋮ Regularity of Lorentzian Busemann Functions ⋮ Mathematical general relativity ⋮ A SURVEY ON GEODESIC COMPLETENESS OF NONDEGENERATE SUBMANIFOLDS IN SEMI-RIEMANNIAN GEOMETRY ⋮ On global hyperbolicity of spacetimes: some recent advances and open problems

Cites Work

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• Splitting theorems for spatially closed space-times
• Decomposition theorems for Lorentzian manifolds with nonpositive curvature
• The splitting theorem for space-times with strong energy condition
• Remarks on cosmological spacetimes and constant mean curvature surfaces
• The Lorentzian splitting theorem without the completeness assumption
• On maximal geodesic-diameter and causality in Lorentz manifolds
• Cut points, conjugate points and Lorentzian comparison theorems
• Curvature, causality and completeness in space-times with causally complete spacelike slices
• The Large Scale Structure of Space-Time

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