AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

A Course in Differential Geometry
Thierry Aubin, University of Paris, France
SEARCH THIS BOOK:

Graduate Studies in Mathematics
2001; 184 pp; hardcover
Volume: 27
ISBN-10: 0-8218-2709-X
ISBN-13: 978-0-8218-2709-3
List Price: US$41
Member Price: US$32.80
Order Code: GSM/27
[Add Item]

Request Permissions

See also:

Curves and Surfaces: Second Edition - Sebastian Montiel and Antonio Ros

This textbook for second-year graduate students is intended as an introduction to differential geometry with principal emphasis on Riemannian geometry. Chapter I explains basic definitions and gives the proofs of the important theorems of Whitney and Sard. Chapter II deals with vector fields and differential forms. Chapter III addresses integration of vector fields and \(p\)-plane fields. Chapter IV develops the notion of connection on a Riemannian manifold considered as a means to define parallel transport on the manifold. The author also discusses related notions of torsion and curvature, and gives a working knowledge of the covariant derivative. Chapter V specializes on Riemannian manifolds by deducing global properties from local properties of curvature, the final goal being to determine the manifold completely. Chapter VI explores some problems in PDEs suggested by the geometry of manifolds.

The author is well known for his significant contributions to the field of geometry and PDEs--particularly for his work on the Yamabe problem--and for his expository accounts on the subject.

The text contains many problems and solutions, permitting the reader to apply the theorems and to see concrete developments of the abstract theory.

Readership

Graduate students, research mathematicians, and mathematics educators interested in differential geometry.

Reviews

"More than half of the book is devoted to exercises, problems at different levels and solutions of exercises. The author's aim was to facilitate the teaching of differential geometry. The presentation is very successful, and I can strongly recommend the book to anybody willing to learn differential geometry, as well as to teachers of the subject."

-- European Mathematical Society Newsletter

"The author is one of the best contemporary geometers and draws from his extended experience in selecting the topics and the various approaches ... It covers topics every working mathematician (or theoretical physicist) ought to know ... The style is very clear and concise, and the emphasis is not on the widest generality, but on the most often encountered situation. This makes it a much more approachable text than many other traditional sources ... an excellent textbook for a first course on basic differential geometry, very helpful to both the instructors and their students."

-- Mathematical Reviews

Table of Contents

  • Background material
  • Differentiable manifolds
  • Tangent space
  • Integration of vector fields and differential forms
  • Linear connections
  • Riemannian manifolds
  • The Yamabe problem-An introduction to research
  • Bibliography
  • Subject index
  • Notation
Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia