John K. Beem

Global Lorentzian Geometry (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 656
• Erscheinungstermin: 29. September 2017
• Englisch
• ISBN-13: 9781351444712
• Artikelnr.: 49377454

Autorenporträt

Beem, John K.

Inhaltsangabe

Introduction - Riemannian themes in Lorentzian geometry
connections and curvature
Lorentzian manifolds and causality
Lorentzian distance
examples of space-times
completness and extendibility
stability of completeness and incompleteness
maximal geodesics and causally disconnected space-times
the Lorentzian cut locus
Morse index theory on Lorentzian manifolds
some results in global Lorentzian geometry
singularities
gravitational plane wave space-times
the splitting problem in global Lorentzian geometry. Appendices: Jacobi Fields and Toponogov's theorem for Lorentzian manifolds
from the Jacobi, to a Riccati, to the Raychaudhuri equation - Jacobi Tensor Fields and the exponential map revisited.