Comparison Theorems in Riemannian Geometry (Paperback)
Language: English
Published by American Mathematical Society, Providence, 2025
- Softcover
- New
Seller: Grand Eagle Retail, Bensenville, IL, U.S.A.Grand Eagle Retail
AbeBooks seller since October 12, 2005
Condition: New
£ 81.04
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Paperback. The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry. Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field. Explore the intricate interplay between curvature, topology, and global geometry in complete Riemannian manifolds. Early chapters introduce foundational aspects like Riemannian geometry, Toponogov's theorem, homogeneous spaces, and Morse theory, while later sections analyze rigidity phenomena and pivotal results from 19591974. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. …
Seller Inventory # 9781470481117
- Title
- Comparison Theorems in Riemannian Geometry (Paperback)
- Author
- Jeff Cheeger
- Publisher
- American Mathematical Society, Providence
- Publication year
- 2025
- Condition
- new
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1470481111
- ISBN 13
- 9781470481117
"Synopsis" may belong to another edition of this title.
About the Author
David G. Ebin, State University of New York at Stony Brook, NY
"About the title" may belong to another edition of this title.
Grand Eagle Retail
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AbeBooks seller since October 12, 2005
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