A Panoramic View of Riemannian Geometry

Marcel Berger

824 pages, parution le 21/08/2003

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Résumé

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.

Euclidean geometry
Transition
Surfaces from Gauss to today
Riemann's Blueprints
A one page panorama
Metric geometry and curvature
Volumes and inequalities on volumes of cycles
Transition: the next two chapters
Spectrum of the Laplacian
Geodesic Dynamics
Best Metrics
From curvature to topology
Holonomy groups and kähler manifolds
Some other important topics
The technical chapter

L'auteur - Marcel Berger

Marcel Berger est directeur de recherches émérite au CNRS. Il a été professeur des universités à Strasbourg, Nice et Paris et directeur de l'Institut des Hautes études scientifiques (IHES). Il a fondé l'école française contemporaine de géométrie différentielle.

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Géométrie 1

Géométrie

Géométrie différentielle

Convexité dans le plan, dans l'espace et au-delà - Volume 2

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer - Printemps des maths, Springer
Auteur(s)	Marcel Berger
Parution	21/08/2003
Nb. de pages	824
Format	16 x 24
Couverture	Relié
Poids	1360g
Intérieur	Noir et Blanc
EAN13	9783540653172