A Panoramic View of Riemannian Geometry

Marcel Berger ()
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Marcel Berger: Institut des Hautes Études Scientifiques IHES

in Springer Books from Springer

Date: 2003
ISBN: 978-3-642-18245-7
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Chapters in this book:

Ch 1 Old and New Euclidean Geometry and Analysis

Marcel Berger

Ch 2 Transition: The Need for a More General Framework

Marcel Berger

Ch 3 Surfaces from Gauß to Today

Marcel Berger

Ch 4 Riemann’s Blueprints for Architecture in Myriad Dimensions

Marcel Berger

Ch 5 A One Page Panorama

Marcel Berger

Ch 6 Riemannian Manifolds as Metric Spaces and the Geometric Meaning of Sectional and Ricci Curvature

Marcel Berger

Ch 7 Volumes and Inequalities on Volumes of Cycles

Marcel Berger

Ch 8 Transition: The Next Two Chapters

Marcel Berger

Ch 9 Riemannian Manifolds as Quantum Mechanical Worlds: The Spectrum and Eigenfunctions of the Laplacian

Marcel Berger

Ch 10 Riemannian Manifolds as Dynamical Systems: the Geodesic Flow and Periodic Geodesics

Marcel Berger

Ch 11 What is the Best Riemannian Metric on a Compact Manifold?

Marcel Berger

Ch 12 From Curvature to Topology

Marcel Berger

Ch 13 Holonomy Groups and Kähler Manifolds

Marcel Berger

Ch 14 Some Other Important Topics

Marcel Berger

Ch 15 The Technical Chapter

Marcel Berger

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DOI: 10.1007/978-3-642-18245-7

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