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General Relativity and the Einstein Equations$
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Yvonne Choquet-Bruhat

Print publication date: 2008

Print ISBN-13: 9780199230723

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199230723.001.0001

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Lorentz Geometry

Lorentz Geometry

Chapter:
(p.1) I Lorentz Geometry
Source:
General Relativity and the Einstein Equations
Author(s):

Yvonne Choquet-Bruhat

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230723.003.0001

This chapter presents a survey of the basic definitions of Riemannian and Lorentzian differential geometry used in this book. The first nine sections use the simplest formulations, in local coordinates, as they are needed for the first five chapters and physical applications. The later sections contain material used in the following, more advanced, chapters. Topics covered include manifolds, differential mappings, vectors and tensors, pseudo-Riemannian metrics, Riemannian connection, geodesics, curvature, geodesic deviation, maximum length and conjugate points, linearized Ricci and Einstein tensors, and second derivative of the Ricci tensor.

Keywords:   Lorentz, Riemann, differential geometry, curvature, geodesic deviation, Ricci tensor

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