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A panoramic view of Riemannian geometry

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Cover of 'A panoramic view of Riemannian geometry'

Table of Contents

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    Book Overview
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    Chapter 1 Old and New Euclidean Geometry and Analysis
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    Chapter 2 Transition: The Need for a More General Framework
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    Chapter 3 Surfaces from Gauß to Today
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    Chapter 4 Riemann’s Blueprints for Architecture in Myriad Dimensions
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    Chapter 5 A One Page Panorama
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    Chapter 6 Riemannian Manifolds as Metric Spaces and the Geometric Meaning of Sectional and Ricci Curvature
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    Chapter 7 Volumes and Inequalities on Volumes of Cycles
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    Chapter 8 Transition: The Next Two Chapters
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    Chapter 9 Riemannian Manifolds as Quantum Mechanical Worlds: The Spectrum and Eigenfunctions of the Laplacian
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    Chapter 10 Riemannian Manifolds as Dynamical Systems: the Geodesic Flow and Periodic Geodesics
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    Chapter 11 What is the Best Riemannian Metric on a Compact Manifold?
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    Chapter 12 From Curvature to Topology
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    Chapter 13 Holonomy Groups and Kähler Manifolds
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    Chapter 14 Some Other Important Topics
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    Chapter 15 The Technical Chapter
Attention for Chapter 10: Riemannian Manifolds as Dynamical Systems: the Geodesic Flow and Periodic Geodesics
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