章节目录
1.Euclidean Geometry — "Old and New Euclidean Geometry and Analysis" 2. Transition — "The Need for a More General Framework" 3. Surfaces from Gauss to Today 4. Riemann's Blueprints — "Riemann's Blueprints for Architecture in Myriad Dimensions" 5. A One Page Panorama 6. Metric Geometry and Curvature — "Riemannian Manifolds as Metric Spaces and the Geometric Meaning of Sectional and Ricci Curvature" 7. Volume and Inequalities on Volumes of Cycles 8. Transition: The Next Two Chapters 9.Spectrum of the Laplacian — "Riemannian Manifolds as Quantum Mechanical Worlds: The Spectrum and Eigenfunctions of the Laplacian" 10. Geodesic Dynamics — "Riemannian Manifolds as Dynamical Systems: the Geodesic Flow and Periodic Geodesics" 11. Best Metric — "What is the Best Riemannian Metric on a Compact Manifold?" 12. From Curvature to Topology 13. Holonomy Groups and Kähler Manifolds 14. Some Other Important Topics 15. The Technical Chapter
内容简介
This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field. From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS
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