微分几何中的初等论题 英文PDF电子书下载

Chapter 1 Graphs and Level Sets 1

Chapter 2 Vector Fields 6

Chapter 3 The Tangent Space 13

Chapter 4 Surfaces 16

Chapter 5 Vector Fields on Surfaces;Orientation 23

Chapter 6 The Gauss Map 31

Chapter 7 Geodesics 38

Chapter 8 Parallel Transport 45

Chapter 9 The Weingarten Map 53

Chapter 10 Curvature of Plane Curves 62

Chapter 11 Arc Length and Line Integrals 68

Chapter 12 Curvature of Surfaces 82

Chapter 13 Convex Surfaces 95

Chapter 14 Parametrized Surfaces 108

Chapter 15 Local Equivalence of Surfaces and Parametrized Surfaces 121

Chapter 16 Focal Points 132

Chapter 17 Surface Area and Volume 139

Chapter 18 Minimal Surfaces 156

Chapter 19 The Exponential Map 163

Chapter 20 Surfaces with Boundary 177

Chapter 21 The Gauss-Bonnet Theorem 190

Chapter 22 Rigid Motions and Congruence 210

Chapter 23 Isometries 220

Chapter 24 Riemannian Metrics 231

Bibliography 245

Notational Index 247

Subject Index 249