Graduate Texts in Mathematics

Introduction to Riemannian Manifolds

Authors: Lee, John

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  • 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
  • Adapted from Riemannian Manifolds, the new edition has been aptly expanded to cover one or two semesters
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eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-91755-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA in USD
  • ISBN 978-3-319-91754-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

​This textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. The second edition has been adapted, expanded, and aptly retitled from Lee’s earlier book, Riemannian Manifolds: An Introduction to Curvature.  Numerous exercises and problem sets provide the student with opportunities to practice and develop skills; appendices contain a brief review of essential background material.
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)

About the authors

​John "Jack" M. Lee is a professor of mathematics at the University of Washington. Professor Lee is the author of three highly acclaimed Springer graduate textbooks : Introduction to Smooth Manifolds, (GTM 218) Introduction to Topological Manifolds (GTM 202), and Riemannian Manifolds (GTM 176). Lee's research interests include differential geometry, the Yamabe problem, existence of Einstein metrics, the constraint equations in general relativity, geometry and analysis on CR manifolds.   

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Table of contents (12 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-91755-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA in USD
  • ISBN 978-3-319-91754-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Riemannian Manifolds
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
176
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-91755-9
DOI
10.1007/978-3-319-91755-9
Hardcover ISBN
978-3-319-91754-2
Series ISSN
0072-5285
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