A Panoramic View of Riemannian Geometry

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Marcel Berger is Ancien Professeur of the University of Paris and emeritus director of research at the Centre National de la Recherche Scientifique (CNRS), from 1979 to 1981 he was president of the French Mathematical Society and from 1985 to 1994 director of the Institut des Hautes Études Scientifiques (IHÉS) in Bures-sur-Yvette.

Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2012
Fachbereich:	Geometrie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xxiii 824 S.
ISBN-13:	9783642621215
ISBN-10:	364262121X
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Berger, Marcel
Auflage:	Softcover reprint of the original 1st edition 2003
Hersteller:	Springer Springer Gabler Springer-Verlag GmbH
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 46 mm
Von/Mit:	Marcel Berger
Erscheinungsdatum:	14.11.2012
Gewicht:	1,264 kg