Books in Geometry

Semi-Riemannian Geometry With Applications to Relativity

1st Edition
Volume 103
June 28, 1983
Barrett O'Neill
English
Hardback
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eBook
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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.

Differential Geometry, Lie Groups, and Symmetric Spaces

1st Edition
Volume 80
February 9, 1979
Sigurdur Helgason
English
eBook
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The present book is intended as a textbook and reference work on three topics in the title. Together with a volume in progress on "Groups and Geometric Analysis" it supersedes my "Differential Geometry and Symmetric Spaces," published in 1962. Since that time several branches of the subject, particularly the function theory on symmetric spaces, have developed substantially. I felt that an expanded treatment might now be useful.

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Books in Geometry

Semi-Riemannian Geometry With Applications to Relativity

Differential Geometry, Lie Groups, and Symmetric Spaces