Overview
Easy for instructors to adapt the topical coverage to suit their course
Develops an intimate acquaintance with the geometric meaning of curvature
Gives students strong skills via numerous exercises and problem sets
Part of the book series: Graduate Texts in Mathematics (GTM, volume 176)
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Table of contents (12 chapters)
Keywords
About this book
While demonstrating the uses of most of the main technical tools needed for a careful study of Riemannian manifolds, this text focuses on ensuring that the student develops an intimate acquaintance with the geometric meaning of curvature. The reasonably broad coverage begins with a treatment of indispensable tools for working with Riemannian metrics such as connections and geodesics. Several topics have been added, including an expanded treatment of pseudo-Riemannian metrics, a more detailed treatment of homogeneous spaces and invariant metrics, a completely revamped treatment of comparison theory based on Riccati equations, and a handful of new local-to-global theorems, to name just a few highlights.
Reviews of the first edition:
Arguments and proofs are written down precisely and clearly. The expertise of the author is reflected in many valuable comments and remarks on the recent developments of the subjects. Serious readers would have the challenges of solving the exercises and problems. The book is probably one of the most easily accessible introductions to Riemannian geometry. (M.C. Leung, MathReview)
The book’s aim is to develop tools and intuition for studying the central unifying theme in Riemannian geometry, which is the notion of curvature and its relation with topology. The main ideas of the subject, motivated as in the original papers, are introduced here in an intuitive and accessible way…The book is an excellent introduction designed for a one-semester graduate course, containing exercises and problems which encourage students to practice working with the new notions and develop skills for later use. By citing suitable references for detailed study, the reader is stimulated to inquire into further research. (C.-L. Bejan, zBMATH)
Reviews
“This material is carefully developed and several useful examples and exercises are included in each chapter. The reviewer’s belief is that this excellent edition will become soon a standard text for several graduate courses as well as an frequent citation in articles.” (Mircea Crâşmăreanu, zbMATH 1409.53001, 2019)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Introduction to Riemannian Manifolds
Authors: John M. Lee
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-319-91755-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-91754-2Published: 14 January 2019
Softcover ISBN: 978-3-030-80106-9Published: 05 August 2021
eBook ISBN: 978-3-319-91755-9Published: 02 January 2019
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 2
Number of Pages: XIII, 437
Number of Illustrations: 210 b/w illustrations
Additional Information: Originally published with title "Riemannian Manifolds: An Introduction to Curvature"
Topics: Differential Geometry