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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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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 21 June 2021

Lorentz Geometry

Lorentz Geometry

(p.1) I Lorentz Geometry
General Relativity and the Einstein Equations

Yvonne Choquet-Bruhat

Oxford University Press

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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