27 Thierry Aubin, A course in differential geometry, 26 Rolf Berndt, An introduction to symplectie geometry, 25 Thomas } iedrich, Dirac operators in . A Course in Differential Geometry (Graduate Studies in Mathematics). Pages · · MB · Downloads ·English. by Thierry Aubin. Preview. Thierry Aubin. Chapter III concerns integration of vector fields. then extends top- plane fields. We cite in particular the interesting proof of the Frobenius theorem.
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A Course in Differential Geometry (Graduate Studies in Mathematics)
Aubim Studies in Mathematics Volume: 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.
A Course in Differential Geometry
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.
A Course in 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 courxe, very helpful to both geometey instructors and their students.
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