Semi-Riemann Geometry and General Relativity
by Shlomo Sternberg
Number of pages: 251
This book represents course notes for a one semester course at the undergraduate level giving an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus, preferably in the language of differential forms.
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by Marcel Berger - Springer
In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. The book offers a great opportunity to get a first impression of some part of Riemannian geometry, together with hints for further reading.
by David R. Wilkins - Trinity College, Dublin
From the table of contents: Smooth Manifolds; Tangent Spaces; Affine Connections on Smooth Manifolds; Riemannian Manifolds; Geometry of Surfaces in R3; Geodesics in Riemannian Manifolds; Complete Riemannian Manifolds; Jacobi Fields.
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An introduction to the geometry of compact Riemann surfaces. Contents: Riemann surfaces; Functions and forms on Riemann surfaces; Abel map, Jacobian and Theta function; Riemann-Roch; Moduli spaces; Eigenvector bundles and solutions of Lax equations.
by John Douglas Moore - University of California
Foundations of Riemannian geometry, including geodesics and curvature, as well as connections in vector bundles, and then go on to discuss the relationships between curvature and topology. Topology will presented in two dual contrasting forms.