Comparison Theorems in Riemannian Geometry (Paperback)

Idioma: inglés

Editorial: American Mathematical Society, Providence, 2025

1470481111 / 9781470481117

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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 our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

N° de ref. del artículo 9781470481117

Título
Comparison Theorems in Riemannian Geometry (Paperback)
Autor
Jeff Cheeger
Editorial
American Mathematical Society, Providence
Año de publicación
2025
Estado
new
Encuadernación
Paperback
Idioma
inglés
ISBN 10
1470481111
ISBN 13
9781470481117

AussieBookSeller

Truganina, VIC, Australia

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Primer artículoEUR 31,90EUR 37,93
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