Comparison Theorems in Riemannian Geometry

Lingua: inglese

Editore: American Mathematical Society, US, 2025

1470481111 / 9781470481117

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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.

Codice articolo LU-9781470481117

Titolo
Comparison Theorems in Riemannian Geometry
Autore
Jeff Cheeger, David G. Ebin
Editore
American Mathematical Society, US
Anno di pubblicazione
2025
Condizione
New
Rilegatura
Paperback
Lingua
inglese
ISBN 10
1470481111
ISBN 13
9781470481117

Rarewaves.com UK

London, Regno Unito

Venditore con 5 stelle

Venditore AbeBooks dal 11 giugno 2025

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ArticoloDa 60 a 60 giorni lavorativiDa 60 a 60 giorni lavorativi
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