Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds

DOI10.1007/BF01303279zbMath0436.53043WikidataQ115393722 ScholiaQ115393722MaRDI QIDQ1140878

Paul E. Ehrlich, Carmen C. Chicone

Publication date: 1980

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/154708

zbMATH Keywords

Riemannian manifoldconjugate pointsLorentzian manifoldcomplete geodesicMorse index theorycomplete nonspacelike geodesic

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global Riemannian geometry, including pinching (53C20)

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Cites Work

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• Some examples of incomplete space-times
• When is a geodesic flow of Anosov type, I
• Riemannian manifolds with geodesic flow of Anosov type
• A theorem of E. Hopf
• What is a singularity in general relativity?
• On complete open manifolds of positive curvature
• The splitting theorem for manifolds of nonnegative Ricci curvature
• Cut points, conjugate points and Lorentzian comparison theorems
• Singularities, incompleteness and the Lorentzian distance function
• The singularities of gravitational collapse and cosmology
• The Large Scale Structure of Space-Time
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