Semi-Riemannian Geometry with Applications to Relativity

This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry )--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.

List of contents

Manifold Theory. Tensors. Semi-Riemannian Manifolds. Semi-Riemannian Submanifolds. Riemannian and Lorenz Geometry. Special Relativity. Constructions. Symmetry and Constant Curvature. Isometries. Calculus of Variations. Homogeneous and Symmetric Spaces. General Relativity. Cosmology. Schwarzschild Geometry. Causality in Lorentz Manifolds. Fundamental Groups and Covering Manifolds. Lie Groups. Newtonian Gravitation.

About the author

Barrett O'Neill is currently a Professor in the Department of Mathematics at the University of California, Los Angeles. He has written two other books in advanced mathematics.

Product details

• Authors: Barrett Neill, O&apos, Barrett O'Neill, Barrett (University of California O'Neill, O'Neill Barrett
• Publisher: Academic Press London
• Languages: English
• Product format: Hardback
• Released: 29.07.1983
• EAN: 9780125267403
• ISBN: 978-0-12-526740-3
• Dimensions: 165 mm x 240 mm x 30 mm
• Series: Pure and Applied Mathematics; Pure and Applied Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Theoretical physics; MATHEMATICS / Geometry / Differential, SCIENCE / Physics / Relativity, Relativity physics, Differential & Riemannian geometry, Differential and Riemannian geometry