文件名称：DIFFERENTIAL GEOMETRY: A First Course in Curves and Surfaces
文件大小：1.71MB
文件格式：PDF
更新时间：2012-03-31 01:19:22
DIFFERENTIAL GEOMETRY, curve, surface
CONTENTS 1. CURVES 1. Examples, Arclength Parametrization 1 2. Local Theory: Frenet Frame 10 3. Some Global Results 22 2. SURFACES: LOCAL THEORY . 1. Parametrized Surfaces and the First Fundamental Form 35 2. The Gauss Map and the Second Fundamental Form 44 3. The Codazzi and Gauss Equations and the Fundamental Theorem of Surface Theory 56 4. Covariant Differentiation, Parallel Translation, and Geodesics 65 3. SURFACES: FURTHER TOPICS 1. Holonomy and the Gauss-Bonnet Theorem 76 2. An Introduction to Hyperbolic Geometry 3. Surface Theory with Differential Forms 4. Calculus of Variations and Surfaces of Constant Mean Curvature 103