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Riemannian geometry during the second half of the twentieth century

Author: Marcel Berger
Publisher: Providence, R.I. : American Mathematical Society, ©2000.
Series: University lecture series (Providence, R.I.), 17.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"In this book, Berger provides a survey of the main developments in Riemannian geometry in the last fifty years, focusing his main attention on the following five areas: Curvature and topology; the construction of and the classification of space forms; distinguished metrics, especially Einstein metrics; eigenvalues and eigenfunctions of the Laplacian; the study of periodic geodesics and the geodesic flow. Other  Read more...
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Document Type: Book
All Authors / Contributors: Marcel Berger
ISBN: 0821820524 9780821820520
OCLC Number: 41540225
Notes: Originally published: Stuttgart : B.G. Teubner, ©1998 (Jahresbericht der Deutschen Mathematiker-Vereinigung ; Bd. 100, Heft 2).
Description: ix, 182 pages ; 26 cm.
Contents: Riemannian Geometry up to 1950. Gauss, Riemann, Christoffel and Levi-Civita. Van Mangoldt, Hadamard, Elie Cartan and Heinz Hopf. Synge, Myers, Preissmann: The use of geometric tools. Hodge, harmonic forms and the Bochner technique: The use of analysis. Allendoerfer, Weil and Chern. Existing tools and a brief look at the new ones. Existing examples and a brief look at the new ones --
Curvature and Topology. Pinching Problems. Curvature of a given sign. Finiteness, compactness, collapsing and the space of all Riemannian structures --
The Geometrical Hierarchy of Riemannian Manifolds: Space Forms. The constant curvature case. Space forms of rank one. Space forms of symmetric spaces of rank larger than one.
Series Title: University lecture series (Providence, R.I.), 17.
Responsibility: Marcel Berger.

Abstract:

Offers a survey of the developments in Riemannian geometry. This book focuses on five areas of Riemannian geometry: Curvature and topology; the construction of and the classification of space forms;  Read more...

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This is quite an amazing book. Bulletin of the London Mathematical Society

 
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