by Luther Pfahler Eisenhart
Publisher: Princeton University Press 1968
Number of pages: 316
The recent physical interpretation of intrinsic differential geometry of spaces has stimulated the study of this subject. This book aims to present the existing theory. Throughout the book constant use is made of the methods of tensor analysis and the Absolute Calculus of Ricci and Levi-Civita.
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by Richard L. Bishop - arXiv
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It starts with the definition of Riemannian and semi-Riemannian structures on manifolds.
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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.
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Course notes for 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.
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A pedagogical but concise overview of Riemannian geometry is provided in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions and relevant theorems.