Differential Geometry of Curves and Surfaces, revised & updated second edition, by Manfredo P. Do Carmo
章節 題號
1-3 Regular Curves; Arc Length 2a, 2b, 6, 7b, 8, 10 1-4 The Vector Product in R3 1, 2, 3, 4, 6, 7, 8 1-5 The Local Theory of Curves Parametrized by
Arc Length
1, 2, 3, 4, 7, 8, 9, 12, 13, 15, 16, 17
1-6 The Local Canonical Form 1, 2a
1-7 Global Properties of Plane Curves 1, 2, 4, 5, 8, 9 2-2 Regular Surfaces; Inverse Images of Regular
Values 1, 2, 3, 4, 5, 7, 8, 9, 11a, 11b
2-3 Change of Parameters; Differentiable Functions
on Surface 1, 2, 3, 5, 6, 7, 14, 15
2-4 The Tangent Plane; The Differential of a Map 1, 2, 3, 4, 12, 13a, 13b, 17, 21, 22
2-5 The First Fundamental Form; Area 1, 5, 8, 9, 12, 14a 3-2 The Definition of the Gauss Map and Its
Fundamental Properties 2, 3, 4, 5, 8, 17
3-3 The Gauss Map in Local Coordinates 1, 2, 3, 5a, 5b, 7a, 16, 20, 21a, 21b
4-2 Isometries; Conformal Maps 1, 2, 3, 4, 9a, 9b, 10, 11a, 11c, 12 4-3 The Gauss Theorem and the Equations of
Compatibility 1, 2, 4, 6, 7, 8, 9
4-4 Parallel Transport; Geodesics 1a, 2, 4, 5, 6, 8 4-5 The Gauss-Bonnet Theorem and Its
Applications 1, 3, 4a, 4b, 5, 6a, 6d
