A COURSE IN DIFFERENTIAL GEOMETRY THIERRY AUBIN PDF

A Course in Differential Geometry. Thierry Aubin. This textbook for 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 IV develops the notion of connection on a Riemannian manifold considered as a means to define parallel transport on the manifold.

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Libraries and resellers, please contact cust-serv ams. See our librarian page for additional eBook ordering options. 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 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.

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

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. 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. Know that ebook versions of most of our titles are still available and may be downloaded immediately after purchase.

AMS Homepage. Join our email list. Sign up. Ordering on the AMS Bookstore is limited to individuals for personal use only. A Course in Differential Geometry Share this page. Advanced search. Author s Product display : Thierry Aubin. Abstract: This textbook for second-year graduate students is intended as an introduction to differential geometry with principal emphasis on Riemannian geometry.

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Dual Price 1: Dual Price 2: Print Available to Order: true. 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. Related Products:. Background Material Chapter 0. Background Material.

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Thierry Aubin

Libraries and resellers, please contact cust-serv ams. See our librarian page for additional eBook ordering options. 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 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.

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A Course in Differential Geometry

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