A Panoramic View of Riemannian Geometry [Hardcover]

Marcel Berger (Author)

Book Description

ISBN-10: 3540653171 | ISBN-13: 978-3540653172 | Publication Date: September 6, 2007

This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field. From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS

Editorial Reviews

Review

From the reviews: "In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. … the book offers a great opportunity to get a first impression of some part of Riemannian geometry, together with hints for further reading." (A.Cap, Monatshefte für Mathematik, Vol. 145 (4), 2005) "Riemannian geometry has become a vast subject, influencing, famously, the development of general relativity and, more recently, the classification of 3-manifolds by hyperbolic structures … . Marcel Berger’s book is an overview of this enormous subject. … Virtually everything is illustrated with clear and useful diagrams … . This is the sort of book one could dip into or refer to over a period of years." (Peter Giblin, The Mathematical Gazette, March, 2005) "Marcel Berger’s A Panoramic View of Riemannian Geometry is without doubt the most comprehensive, original and idiosyncratic treatise on differential geometry … . he manages to include the most up-to-date references on even the most classical topics that he presents, and he puts far greater emphasis on applications. … the book concludes with a massive and extremely useful bibliography of 1310 items." (Robert Osserman, SIAM Review, Vol. 47 (1), 2005) "This book of one of the main contributors to Riemannian geometry has as a first goal to give an overview to most of the living topics of the subject. … A second goal is to show how many intuitive geometric questions lead to Riemannian geometry in a natural way. In my opinion it is this way of explaining … which makes the book highly recommendable to students as well as to experienced geometers. Furthermore, this book is clearly an encyclopedia in Riemannian geometry … ." (F.Manhart, Internationale Mathematische Nachrichten, Issue 197, 2004) "This book is really a panorama. … the reading creates pleasure for the interested reader. … the book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." (Jürgen Eichhorn, Mathematical Reviews, 2004 h) "Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. … enables the reader to obtain a sweeping panoramic view of almost the entirety of the field." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 49 (3-4), 2003)

Product Details

• Hardcover: 875 pages
• Publisher: Springer (September 6, 2007)
• Language: English
• ISBN-10: 3540653171
• ISBN-13: 978-3540653172
• Product Dimensions: 9.6 x 6.6 x 2 inches
• Shipping Weight: 2.8 pounds (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #102,055 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

8 of 8 people found the following review helpful:

5.0 out of 5 stars A superb, rigorous overview of the topic, but without the proofs, May 1, 2009

By 

J. Scales (Colorado) - See all my reviews
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This review is from: A Panoramic View of Riemannian Geometry (Kindle Edition)

This is a beautifully written survey of a wide swath of modern mathematics and mathematical physics related to Riemannian geometry. For a non-expert, like me, it allowed me to get a broad perspective on the field without having to struggle through so many proofs. The explanations are clear and rigorous (two goals which are frequently in conflict). There is a vast bibliography as well. A number of problems I was familiar with in other contexts turn out to have unplumbed (by me at least) geometrical significance. All in all, a wonderful book.

2 of 2 people found the following review helpful:

5.0 out of 5 stars Wonderful overview!, August 25, 2010

By 

Tom Dickens (Houston, TX USA) - See all my reviews

This review is from: A Panoramic View of Riemannian Geometry (Hardcover)

Excellent exposition of a wide variety of topics in geometry for the non-expert like me. It helped me get a better grasp of a number of differential geometric structures that are used in theoretical physics these days, without having to wade through a bunch of proofs. The list of references is immense, so that the reader can follow up with more detailed, and more rigorous, material for topics of choice. Highly recommended for mathematicians and physicists alike.

8 of 27 people found the following review helpful:

4.0 out of 5 stars A fine book., June 23, 2004

By 

Hiro (SLC, UT) - See all my reviews

This review is from: A Panoramic View of Riemannian Geometry (Hardcover)

This book is a good reference for anyone who wants to know about the development of riemannian geometry. It covers many active topics in modern differential geometry for every graduated students who can choose some interested fields for the thesis.