UID:
almahu_9947363023202882
Format:
XXIII, 824 p.
,
online resource.
ISBN:
9783642182457
Content:
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.
Note:
1 Euclidean Geometry -- 2 Transition -- 3 Surfaces from Gauß to Today -- 4 Riemann’s Blueprints -- 5 A One Page Panorama -- 6 Metric Geometry and Curvature -- 7 Volumes and Inequalities on Volumes of Cycles -- 8 Transition: The Next Two Chapters -- 9 Spectrum of the Laplacian -- 10 Geodesic Dynamics -- 11 Best Metrics -- 12 From Curvature to Topology -- 13 Holonomy Groups and Kähler Manifolds -- 14 Some Other Important Topics -- 15 The Technical Chapter -- References -- Acknowledgements -- List of Notation -- List of Authors.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9783540653172
Language:
English
DOI:
10.1007/978-3-642-18245-7
URL:
http://dx.doi.org/10.1007/978-3-642-18245-7
URL:
Volltext
(lizenzpflichtig)
