Differential Geometry (Paperback)

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Editorial Reviews

Product Description

An introductory textbook on the differential geometry of curves and surfaces in three-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods and results involved. With problems at the end of each section, and solutions listed at the end of the book. 99 illustrations.

Language Notes

Text: English (translation)
Original Language: German

Product Details

• Paperback: 366 pages
• Publisher: Dover Publications; 1 edition edition (June 1, 1991)
• Language: English
• ISBN-10: 0486667219
• ISBN-13: 978-0486667218
• Product Dimensions: 8.3 x 5.4 x 0.8 inches
• Shipping Weight: 12.8 ounces (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (16 customer reviews)
• Amazon.com Sales Rank: #242,657 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

71 of 72 people found the following review helpful:

5.0 out of 5 stars Agree -- one of the best; elegant; beautiful, March 19, 2004

By	Paul J. Papanek "latoxdoc" (Los Angeles, CA United States) - See all my reviews (REAL NAME)

I had been seeking a book on differential geometry for self-study, as a preface to learning general relativity. A seasoned mathematics friend recommended Kreyszig.

So, I waded in, and patiently made my way through every page of the first six chapters, working the problems along the way, at a pace of a few pages per day. Now that the journey is behind me, I can say that I appreciated this book. It compares favorably to some other texts I had tried reading, with less success.

I realize that the author's approach is an old-style classical one, with a reliance on specific coordinate systems and transformations between coordinate systems. To work the problems requires a fair amount of paper and pencil work. Nonetheless, this approach worked well for me. On those occasions when my reading bogged down, inevitably there was a good reason. If I went back carefully, re-read and pondered, doodled on paper, and tried to visualize what Kreyszig was describing, it always worked! The light would soon go on, usually with a pleasurable sense of discovery.

I went back to re-read certain sections of the book to refresh my memory, and realized how elegant the writing is. Crystal clear, right to the heart, and always trustworthy. Everything follows in a gentle persuasive way; there are no jarring leaps or gaps.

Additionally, I had a nice sense of the different flavor brought to the field by the French geometers who made many of the key advances around the turn of the 19th-20th century.

Finally, the summary of key results and equations at the end is very smart and helpful.

Since finishing Kreysig, I did find it helpful to push on and try to grasp these same ideas from the standpoint of one-forms and the coordinate-free approach to tensors. But I'm not sorry I came at the subject this way first.

I do recommend this book, and think that a beginner needs only a moderate amount of stamina and patience here.

A postscript -- the book is also beautiful. I like that in a math book.

42 of 42 people found the following review helpful:

5.0 out of 5 stars By far the best intro to classical differential geometry, May 24, 2001

By	Muraari Vasudevan (Everett, WA USA) - See all my reviews (REAL NAME)

This is the sort of math book that you pick up, get something to drink, sit on the couch and read through as you would read a novel. I dont know if its possible to write a simpler or clearer treatment on differential geomerty. But be warned that it is still only "classical". Tensros are treated as objects that tranform in a certain way, rather than studied as general multilinear functions. However, after reading this book, any book on tensors is a breeeze to go through. Well worth having, especially considering the price.

42 of 45 people found the following review helpful:

5.0 out of 5 stars highly recommended, August 1, 2002

By	ubuntu (USA) - See all my reviews

This is a wonderfully well written book. If you have a good background in calculus and analytic geometry, you will have no problems with understanding most of the book. (If you don't, you shouldn't be studying differential geometry anyway.) The last couple of chapters are more difficult. Make sure to do the problems after each chapter; they are very well designed to enhance your understanding, and as a huge bonus, their solutions can be found at the end of the book. Forget about those books with a fancy hard cover and cost ten times as much. Buy this book and enjoy!