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Comparison Theorems in Riemannian Geometry
Language: English
Published by American Mathematical Society, US, 2025
ISBN 10: 1470481111 ISBN 13: 9781470481117
Seller: Rarewaves.com USA, London, LONDO, United Kingdom
Seller rating 5 out of 5 stars
Paperback. Condition: New. 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.
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Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing)
Book 39 of 63: Ams Chelsea PublishingLanguage: English
Published by American Mathematical Society, 2008
ISBN 10: 0821844172 ISBN 13: 9780821844175
Seller: Kennys Bookshop and Art Galleries Ltd., Galway, GY, Ireland
Seller rating 5 out of 5 stars
Condition: New. Focuses on the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. This title begins with an introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem. It then gives a presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. Series: AMS Chelsea Publishing. Num Pages: 161 pages, Illustrations. BIC Classification: PBMP; PBPD. Category: (P) Professional & Vocational. Dimension: 261 x 184 x 13. Weight in Grams: 468. . 2008. Hardcover. . . . .
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US$ 78.18
US$ 13.54 shipping
Ships from United Kingdom to U.S.A.Quantity: 2 available
Add to basketPaperback. Condition: Brand New. 162 pages. 5.98x0.98x9.02 inches. In Stock.
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Comparison Theorems in Riemannian Geomet
Language: English
Published by American Mathematical Society, 2025
ISBN 10: 1470481111 ISBN 13: 9781470481117
Condition: New.
-
Comparison Theorems in Riemannian Geometry
Book 39 of 63: Ams Chelsea PublishingLanguage: English
Published by American Mathematical Society, 2008
ISBN 10: 0821844172 ISBN 13: 9780821844175
Condition: New.
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US$ 85.04
US$ 13.54 shipping
Ships from United Kingdom to U.S.A.Quantity: 1 available
Add to basketHardcover. Condition: Brand New. illustrated edition. 161 pages. 10.25x7.25x0.50 inches. In Stock.
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Comparison Theorems in Riemannian Geometry
Book 39 of 63: Ams Chelsea PublishingLanguage: English
Published by American Mathematical Society, 2008
ISBN 10: 0821844172 ISBN 13: 9780821844175
Condition: As New. Unread book in perfect condition.
-
Comparison Theorems in Riemannian Geomet
Language: English
Published by American Mathematical Society, 2025
ISBN 10: 1470481111 ISBN 13: 9781470481117
Condition: As New. Unread book in perfect condition.
-
Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing)
Book 39 of 63: Ams Chelsea PublishingLanguage: English
Published by American Mathematical Society, 2008
ISBN 10: 0821844172 ISBN 13: 9780821844175
Condition: New. Focuses on the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. This title begins with an introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem. It then gives a presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. Series: AMS Chelsea Publishing. Num Pages: 161 pages, Illustrations. BIC Classification: PBMP; PBPD. Category: (P) Professional & Vocational. Dimension: 261 x 184 x 13. Weight in Grams: 468. . 2008. Hardcover. . . . . Books ship from the US and Ireland.
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Comparison Theorems in Riemannian Geometry
Book 39 of 63: Ams Chelsea PublishingLanguage: English
Published by American Mathematical Society, 2008
ISBN 10: 0821844172 ISBN 13: 9780821844175
Seller: GreatBookPricesUK, Woodford Green, United Kingdom
Seller rating 5 out of 5 stars
US$ 84.35
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Ships from United Kingdom to U.S.A.Quantity: 2 available
Add to basketCondition: New.
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Comparison Theorems in Riemannian Geomet
Language: English
Published by American Mathematical Society, 2025
ISBN 10: 1470481111 ISBN 13: 9781470481117
Seller: GreatBookPricesUK, Woodford Green, United Kingdom
Seller rating 5 out of 5 stars
US$ 84.24
US$ 20.30 shipping
Ships from United Kingdom to U.S.A.Quantity: 1 available
Add to basketCondition: New.
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Comparison Theorems in Riemannian Geometry
Language: English
Published by American Mathematical Society, 2025
ISBN 10: 1470481111 ISBN 13: 9781470481117
Condition: New.
-
Comparison Theorems in Riemannian Geometry
Book 39 of 63: Ams Chelsea PublishingLanguage: English
Published by American Mathematical Society, 2008
ISBN 10: 0821844172 ISBN 13: 9780821844175
Seller: GreatBookPricesUK, Woodford Green, United Kingdom
Seller rating 5 out of 5 stars
US$ 99.61
US$ 20.30 shipping
Ships from United Kingdom to U.S.A.Quantity: 2 available
Add to basketCondition: As New. Unread book in perfect condition.
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Comparison Theorems in Riemannian Geomet
Language: English
Published by American Mathematical Society, 2025
ISBN 10: 1470481111 ISBN 13: 9781470481117
Seller: GreatBookPricesUK, Woodford Green, United Kingdom
Seller rating 5 out of 5 stars
US$ 99.59
US$ 20.30 shipping
Ships from United Kingdom to U.S.A.Quantity: 1 available
Add to basketCondition: As New. Unread book in perfect condition.
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Comparison Theorems in Riemannian Geometry
Language: English
Published by American Mathematical Society, US, 2025
ISBN 10: 1470481111 ISBN 13: 9781470481117
US$ 75.47
US$ 87.98 shipping
Ships from United Kingdom to U.S.A.Quantity: 3 available
Add to basketPaperback. Condition: New. 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.
