Splitting theorems for spatially closed space-times

DOI10.1007/BF01212528zbMath0575.53040MaRDI QIDQ1064556

Gregory J. Galloway

Publication date: 1984

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Cauchy surfacesingularity theoremLorentzian splitting theorempseudo-Riemannian producttimelike convergence

Mathematics Subject Classification ID

Relativistic cosmology (83F05) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (19)

Bartnik’s splitting conjecture and Lorentzian Busemann function ⋮ Parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes ⋮ Remarks on cosmological spacetimes and constant mean curvature surfaces ⋮ Regularity of variational maximal surfaces ⋮ Some connections between global hyperbolicity and geodesic completeness ⋮ Curvature, causality and completeness in space-times with causally complete spacelike slices ⋮ The splitting theorem for globally hyperbolic Lorentzian length spaces with non-negative timelike curvature ⋮ Omniscient foliations and the geometry of cosmological spacetimes ⋮ Rigidity and concircular symmetries ⋮ Achronal limits, Lorentzian spheres, and splitting ⋮ Regularity of Lorentzian Busemann Functions ⋮ The Riemannian and Lorentzian Splitting Theorems ⋮ Lines in space-times ⋮ Compact Lorentzian Manifolds Without Closed Nonspacelike Geodesics ⋮ Class A spacetimes ⋮ Geometric analysis of Lorentzian distance function on spacelike hypersurfaces ⋮ Rigidity in vacuum under conformal symmetry ⋮ Some results about the level sets of Lorentzian Busemann function and Bartnik's conjecture ⋮ Some remarks on conformal symmetries and Bartnik's splitting conjecture

Cites Work

• Existence of maximal surfaces in asymptotically flat spacetimes
• H-surfaces in Lorentzian manifolds
• Some results on Cauchy surface criteria in Lorentzian geometry
• On the determination of Cauchy surfaces from intrinsic properties
• Essais de géométrie riemannienne hyperbolique globale. Applications à la relativité générale
• The splitting theorem for manifolds of nonnegative Ricci curvature
• Elliptic Partial Differential Equations of Second Order
• The Large Scale Structure of Space-Time
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