| 约翰·奥普里，美国克利夫兰州立大学数学系教授，从事理论研究多年，并具有丰富的教学经验，主要研究方向为代数拓扑学在几何学上的应用等。 |
| 第1版前言（修订版） 引言 Chapter 1. The Geometry of Curves Introduction Arclength Parametrization Frenet Formulas Nonunit Speed Curves Some Implications of Curvature and Torsion Green’s Theorem and the Isoperimetric Inequality The Geometry of Curves and MAPLE Chapter 2. Surfaces. Introduction The Geometry of Surfaces The Linear Algebra of Surfaces Normal Curvature Plotting Surfaces in MAPLE Chapter 3. Curvatures Introduction Calculating Curvature Surfaces of Revolution A Formula for Gaussian Curvature Some Effects of Curvatures Surfaces of Delaunay Calculating Curvature with MAPLE Chapter 4. Constant Mean Curvature Surfaces Chapter 5. Geodesics， Metrics and Isometries Chapter 6. Holonomy and the Gauss-Bonnet Theorem Chapter 7. The Calculus of Variations and Geometry Chapter 8. A Glimpse at Higher Dimensions Appendix A.Hints and Solutions to Selected Problems References Index |
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