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A Panoramic View of Riemannian Geometry

Author: Marcel Berger
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2003.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. These results are stated without detailed proofs but the main ideas involved are described and motivated. This enables the reader to obtain a sweeping panoramic view of almost the entirety  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Marcel Berger
ISBN: 9783642182457 3642182453 3540653171 9783540653172
OCLC Number: 851821086
Description: 1 online resource (xlvi, 824 pages)
Contents: From the contents: Euclidean Geometry and Analysis: Old but also Some New --
Gauss' Contributions on Surfaces and also some more Recent Things --
What Riemann Did and Other Things --
Metric Properties of Riemannian Manifolds and the Geometric Meaning of Sectional and Ricci Curvature --
Volumes and Isoic Type Inequalities in Riemannian Manifolds --
Riemannian Manifolds as Quantum Mechanic Objects: The Spectrum and the Eigenfunctions of Laplacian --
The Search for Distinguished Metrics: What is the Best Riemannian Metric on a Given Compact Manifold? --
From Curvature to Topology --
Global Parallel Transport and another Riemannian Hierarchy: Holonomy Groups and Kähler Manifolds --
Some other important Topics --
The Technical chapter.
Responsibility: by Marcel Berger.

Abstract:

This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are  Read more...

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From the reviews:"In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. ... the book offers a great opportunity to get a first impression of some Read more...

 
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