دانلود کتاب Elementary Differential Geometry

فهرست مطالب :

Elementary Differential Geometry......Page 3
Preface......Page 5
Contents......Page 8
1. Curves in the plane and in space......Page 11
2. How much does a curve curve?......Page 38
3. Global properties of curves......Page 64
4. Surfaces in three dimensions......Page 75
5. Examples of surfaces......Page 102
6. The first fundamental form......Page 127
7. Curvature of surfaces......Page 164
8. Gaussian, mean and principal curvatures......Page 183
9. Geodesics......Page 218
10. Gauss\' Theorema Egregium......Page 249
11. Hyperbolic geometry......Page 271
12. Minimal surfaces......Page 307
13. The Gauss–Bonnet theorem......Page 336
A0. Inner product spaces and self-adjoint linear maps......Page 379
A1. Isometries of Euclidean spaces......Page 382
A2. Möbius transformations......Page 390
Hints to selected exercises......Page 399
Solutions......Page 404
Index......Page 465