A Panoramic View of Riemannian Geometry
By: by Marcel Berger
Publisher: Springer Berlin Heidelberg
Published: 2003
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 824
ISBN-13: 9783642621215; 9783642182457
Subjects: Global differential geometry; Mathematics
Description: 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 of the field. However, since a Riemannian manifold is, even initially, a subtle object, appealing to highly non-natural concepts, the first three chapters devote themselves to introducing the various concepts and tools of Riemannian geometry in the most natural and motivating way, following in particular Gauss and Riemann.
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Table of contents: title: From the contents: Euclidean Geometry and Analysis: Old but also Some New; title: Gauss' Contributions on Surfaces and also some more Recent Things; title: What Riemann Did and Other Things; title: Metric Properties of Riemannian Manifolds and the Geometric Meaning of Sectional and Ricci Curvature; title: Volumes and Isoic Type Inequalities in Riemannian Manifolds; title: Riemannian Manifolds as Quantum Mechanic Objects: The Spectrum and the Eigenfunctions of Laplacian; title: The Search for Distinguished Metrics: What is the Best Riemannian Metric on a Given Compact Manifold?; title: From Curvature to Topology; title: Global Parallel Transport and another Riemannian Hierarchy: Holonomy Groups and Kähler Manifolds; title: Some other important Topics; title: The Technical chapter.