30-Day No-Hassle Returns
We guarantee your satisfaction on every purchase or rental with a full refund within 30 days of your purchase date.
Fast Customer Service
If you need help, our friendly customer service team is here to help!
The Best Prices on Textbook Rentals, Guaranteed
You can shop with confidence with the best rental prices at ValoreBooks.com. If you find a lower priced rental, we will match it.

Geometry of Manifolds

Author: 


ISBN-13: 

9780821829233


ISBN: 

0821829238


Publisher:  American Mathematical Society
Summary: From the Preface of the First Edition: ''Our purpose in writing this book is to put material which we found stimulating and interesting as graduate students into form. It is intended for individual study and for use as a text for graduate level courses such as the one from which this material stems, given by Professor W. Ambrose at MIT in 1958-1959. Previously the material had been organized in roughly the same form ...by him and Professor I. M. Singer, and they in turn drew upon thework of Ehresmann, Chern, and E. Cartan. Our contributions have been primarily to fill out the material with details, asides and problems, and to alter notation slightly. ''We believe that this subject matter, besides being an interesting area for specialization, lends itself especially to a synthesisof several branches of mathematics, and thus should be studied by a wide spectrum of graduate students so as to break away from narrow specialization and see how their own fields are related and applied in other fields. We feel that at least part of this subject should be of interest not only to those working in geometry, but also to those in analysis, topology, algebra, and even probability and astronomy. In order that this book be meaningful, the reader's background should include realvariable theory, linear algebra, and point set topology.'' This volume is a reprint with few corrections of the original work published in 1964. Starting with the notion of differential manifolds, the first six chapters lay a foundation for the study of Riemannian manifolds through specializing the theoryof connections on principle bundles and affine connections. The geometry of Riemannian manifolds is emphasized, as opposed to global analysis, so that the theorems of Hopf-Rinow, Hadamard-Cartan, and Cartan's local isometry theorem are included, but no elliptic operator theory. Isometric immersions are treated elegantly and from a global viewpoint. In the final chapter are the more complicated estimates on which much of the research in Riemannian geometry is based: the Morse index theorem,Synge's theorems on closed geodesics, Rauch's comparison theorem, and the original proof of the Bishop volume-comparison theorem (with Myer's Theorem as a corollary). The first edition of this book was the origin of a modern treatment of global Riemannian geometry, using the carefully conceived notationthat has withstood the test of time. The primary source material for the book were the papers and course notes of brilliant geometers, including E. Cartan, C. Ehresmann, I. M. Singer, and W. Ambrose. It is tightly organized, uniformly very precise, and amazingly comprehensive for its length.

Bishop, Richard L. is the author of Geometry of Manifolds, published under ISBN 9780821829233 and 0821829238. Two hundred twelve Geometry of Manifolds textbooks are available for sale on ValoreBooks.com, ten used from the cheapest price of $90.97, or buy new starting at $40.00.
 [read more]

Marketplace Prices
202 New from $40.00 10 Used from $90.97
  • Used $90.97
  • New $40.00
Price + Shipping
Condition
Details
Product Details
Geometry of Manifolds

ISBN-13: 9780821829233


ISBN: 0821829238


Publisher: American Mathematical Society
www.ValoreBooks.com is a student's number one resource for cheap Geometry of Manifolds rentals, or used and new condition books that can be mailed to you in no time.
Where's My Stuff?
Shipping & Returns