We prove three facts about intrinsic geometry of surfaces in a normed (Minkowski ) space. When put together, these facts demonstrate a rather intriguing picture. Submission history. From: Sergei Ivanov [view email] [v1] Thu, 5 May 54 UTC (10 KB) [v2] Mon, 6 Jun UTC (11 KB). Submission history. From: Sergei Ivanov [view email] [v1] Mon, 8 Oct 52 UTC (15 KB) [v2] Sun, 23 Jun UTC (16 KB).
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Contributing to this are the many elementary examples with which the authors supplement the text Anyone who is intensely concerned with Riemmannian geometry will not pass up this book.
It is so far without competition and fills a gap in the market. Would you like to tell us about a lower price? If you are a seller for this product, would you like to suggest updates through seller support? This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations.
The objective of this graduate textbook is twofold: The authors tend to work with “easy-to-touch” mathematical objects using “easy-to-visualize” methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students.
Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of exposition.
A Course in Metric Geometry
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Graduate Studies in Mathematics Book 33 Hardcover: American Mathematical Society July Language: I’d like to read this book on Kindle Don’t have a Kindle?
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Burago , Ivanov : On intrinsic geometry of surfaces in normed spaces
Please try again later. I adopted this text for a new graduate course that I taught on Metric Geometry. I chose this text because it has exercises, it appears to cover nonpositive and nonnegative curvature in roughly equal proportion, and it’s less than half the price of Bridson-Haefliger.
Unfortunately, the book has many, many typos. Fortunately, there is an errata consisting of ten pages that can be found by googling “burago burago ivanov errata”.
Actually it’s more than ivznov a list of typos: They correct a few false proofs as well. This list of errors is not complete. My students and I have found other typos as well. Of course, a well-trained mathematician can get past the typos, but this text is supposed to be for first year graduate students. The writing is also rough in places.
For example, polyhedral complexes are not rigorously defined. The style is Russian which I like, but it’s not the best example of this type of writing.
Mathematics > Group Theory
The students have told me that they avoid reading the text whenever possible. The one redeeming feature may be the exercises.
Some of the exercises are excellent. Also the overall choice of topics is very good. With additional work this could be a great textbook, and five years later I am still hoping that the ivwnov will take the time to burxgo through it at least a couple of more times.
For now, I have switched to Bridson-Haefliger. I have abandoned this book. The authors present a self-contained treatment of the geometry of length spaces.
They begin with the definition of length spaces, and by the final chapter cover almost all of the material in the well known survey paper by Burago, Gromov, and Perel’man. Overall, the book provides ubrago interesting and and accessible introduction to an important class of spaces length spaces arise as limits of sequences of Riemannian manifolds.
I found it exceedingly interesting that one can build analogues of most of the concepts from Riemannian geometry using only the intrinsic metric. There is great emphasis on exposition in this book; Burago makes great effort to motivate definitions and provide interesting examples.
The reader is cautioned, however, that numerous typographic errors are to be found some in fundamental definitions. My only complaint is the uneveness of the treatment. It seems unlikely to me that a reader who is interested in length spaces would not already have at least passing aquaintence with Riemannian geometry.
This, however, is a minor point, and I can recommend the book very highly. I am an undergraduate math student, and I encountered this book as the burato background text for a summer project in geometry. It does a number of things very well, but it does possess some comparitively minor flaws that are nonetheless worth noting.
The definitions and examples are very clearly explained and in a manner highly suitable for self-study. Most of the proofs are very well written, and the authors do bursgo good job of demonstrating the appropriate tools and outlining the best approaches in the proofs and the examples. The authors also do a good job in general of summoning the neccessary background material without dwelling on review too extensively; you buraggo probably have already seen the Hausdorff measure and the fundamental group before you pick up this book, but the book recalls the main concepts and results with helpful exercises in case your memory has faded or don’t have much experience with such notions.
Even the review of Riemannian geometry, which might be too long for some, ivvanov appropriate to firmly establish notation and because hyperbolic geometry and Riemannian curvature are so central to the topic of the text. While most of the proofs are ivanoov to follow especially the more technical proofs where lack of clarity would be a serious problemsome of the more visually-oriented proofs are very poorly written and there are precious few diagrams to compensate – see, for example, the example involving the curvature of cones over circles of various lengths.
Also, the book could use some more exercises to accompany the more technical constructions. The exercises that it has ivannov very well-chosen for the purpose of forcing the reader to internalize the relavent concepts and techniques, but some basic definition chasing to help process ivano harder definitions would make the process go smoother.
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