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 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.
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 Curtis McMullen - Harvard University
This course will concern the interaction between: hyperbolic geometry in dimensions 2 and 3, the dynamics of iterated rational maps, and the theory of Riemann surfaces and their deformations. Intended for advanced graduate students.
by Sigmundur Gudmundsson - Lund University
The main purpose of these lecture notes is to introduce the beautiful theory of Riemannian Geometry. Of special interest are the classical Lie groups allowing concrete calculations of many of the abstract notions on the menu.