Differential and Riemannian Manifolds (Graduate Texts in Mathematics)

Buy Now or Get more Details!

Binding: Hardcover
Dewey Decimal Number: 516.36
EAN: 9780387943381
Edition: 3rd
ISBN: 0387943382
Label: Springer
Manufacturer: Springer
Number Of Items: 1
Number Of Pages: 384
Publication Date: March 09, 1995
Publisher: Springer
Studio: Springer


 

Editorial Review:

Product Description:
This is the third version of a book on Differential Manifolds; in this latest expansion three chapters have been added on Riemannian and pseudo-Riemannian geometry, and the section on sprays and Stokes' theorem have been rewritten. This text provides an introduction to basic concepts in differential topology, differential geometry and differential equations. In differential topology one studies classes of maps and the possibility of finding differentiable maps in them, and one uses differentiable structures on manifolds to determine their topological structure. In differential geometry one adds structures to the manifold (vector fields, sprays, a metric, and so forth) and studies their properties. In differential equations one studies vector fields and their integral curves, singular points, stable and unstable manifolds, and the like.

Average Rating:

Rating: - Modern, but....
This book is a proper subset of Lang's later book "Fundamentals of Differential Geometry (Graduate Texts in Mathematics, 191)".

Rating: - Not a "first book", ok as reference
Lang's book is definitely not useful as textbook for classes or for self-guided study (learnt this the hard way). He is rather abstract and provides zero motivation for the theory. The book is obviously made for people who learnt diff. geometry elsewhere but want to read a cleaner and more modern treatment. To this end, Lang's book is useful. The best part is that manifolds are infinite-dimensional right away. This is probably the only reason for buying Lang instead of/in addition to Dieudonne ... Read More

---

Rating: - Maybe Lang's best book.
Well, we have here another book on differential manifolds, and another book by Serge Lang. Lang is well-known by writing (lots of) books on different topics in analysis and algebra, all of them in a quite "Bourbaki-like" style: attaining maximum generality, with less motivation than most students would like. This is no surprise, because Lang himself is a Bourbakist.

So, what's interesting about D&RM? It's a book very much like Lang's other books, only that here the Bourbakist's approach ... Read More