Book 2003

A Panoramic View of Riemannian Geometry


ISBN: 978-3-540-65317-2 (Print) 978-3-642-18245-7 (Online)

Table of contents (15 chapters)

  1. Front Matter

    Pages I-XXIII

  2. Chapter

    Pages 1-99

    Old and New Euclidean Geometry and Analysis

  3. Chapter

    Pages 101-104

    Transition: The Need for a More General Framework

  4. Chapter

    Pages 105-142

    Surfaces from Gauß to Today

  5. Chapter

    Pages 143-218

    Riemann’s Blueprints for Architecture in Myriad Dimensions

  6. Chapter

    Pages 219-219

    A One Page Panorama

  7. Chapter

    Pages 221-297

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

  8. Chapter

    Pages 299-368

    Volumes and Inequalities on Volumes of Cycles

  9. Chapter

    Pages 369-372

    Transition: The Next Two Chapters

  10. Chapter

    Pages 373-429

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

  11. Chapter

    Pages 431-497

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

  12. Chapter

    Pages 499-541

    What is the Best Riemannian Metric on a Compact Manifold?

  13. Chapter

    Pages 543-635

    From Curvature to Topology

  14. Chapter

    Pages 637-657

    Holonomy Groups and Kähler Manifolds

  15. Chapter

    Pages 659-691

    Some Other Important Topics

  16. Chapter

    Pages 693-721

    The Technical Chapter

  17. Back Matter

    Pages 723-824