Global Lorentzian Geometry

2017/09/29 by John K. Beem, Paul E. Ehrlich, Kevin L. Easley · 5 citations
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Relativity and Gravitational Theory #Geometry #Physics #Mathematics

paper · doi:10.1201/9780203753125

openalex publication_date 2017/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/14

Abstract

Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.

Cited by

• Infinitesimal and Local Convexity of a Hypersurface in a Semi-Riemannian Manifold
• Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies
• Polish spaces of causal curves
• New futures for cosmological models
• Warped product space-times
• Pseudo-Euclidean billiards within confocal curves on the hyperboloid of one sheet
• Biharmonic CMC Hypersurfaces in the Warped Product Space
• Comparison theorems on weighted Finsler manifolds and spacetimes with ε-range
• Geometric analysis of particular compactly constructed time machine spacetimes
• Limit curve theorems in Lorentzian geometry
• Splitting theorem [wikipedia]

Related

• Topics in Lorentz Geometry
• Lorentz spacetimes of constant curvature
• A Treatise on Differential Geometry and its role in Relativity Theory
• Geometrical methods in mathematical physics
• General Relativity and the Einstein Equations