Free Book Online
A Course in Differential Geometry (Graduate Studies in Mathematics)


A Course in Differential Geometry (Graduate Studies in Mathematics)

2.3 (1786)

Log in to rate this item

    Available in PDF Format | A Course in Differential Geometry (Graduate Studies in Mathematics).pdf | Unknown
    Thierry Aubin
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.   show more
3.5 (12439)
  • Pdf

*An electronic version of a printed book that can be read on a computer or handheld device designed specifically for this purpose.

Formats for this Ebook

Required Software Any PDF Reader, Apple Preview
Supported Devices Windows PC/PocketPC, Mac OS, Linux OS, Apple iPhone/iPod Touch.
# of Devices Unlimited
Flowing Text / Pages Pages
Printable? Yes

Book details

  • PDF | 184 pages
  • Thierry Aubin
  • American Mathematical Society
  • Unknown
  • 2
  • Science Math

Review Text

The message text:

Other Ebook