A Course in Differential Geometry is popular PDF and ePub book, written by Thierry Aubin in 2001, it is a fantastic choice for those who relish reading online the Geometry, Differential genre. Let's immerse ourselves in this engaging Geometry, Differential book by exploring the summary and details provided below. Remember, A Course in Differential Geometry can be Read Online from any device for your convenience.
A Course in Differential Geometry Book PDF Summary
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.
Detail Book of A Course in Differential Geometry PDF
- Author : Thierry Aubin
- Release : 02 June 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821827093
- Genre : Geometry, Differential
- Total Page : 198 pages
- Language : English
- PDF File Size : 20,5 Mb
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