ОГЛАВЛЕНИЕ

От переводчика                                                                                                  5

Предисловие                                                                                                      7

1. Графики и множества уровня                                                                         11

2. Векторные поля                                                                                             17

3. Касательное пространство                                                                             26

4. Поверхности                                                                                                  30

5. Векторные поля на поверхностях; ориентация                                               39

6. Гауссово отображение                                                                                   50

7. Геодезические                                                                                                59

8. Параллельный перенос                                                                                   69

9. Отображение Вейнгартена                                                                             80

10. Кривизна плоских кривых                                                                            93

11. Длина дуги и криволинейные интегралы                                                     101

12. Кривизна поверхностей                                                                               121

13. Выпуклые поверхности                                                                               140

14. Параметризованные поверхности                                                                160

15. Локальная эквивалентность поверхностей и параметризованных поверхностей 176

16. Фокальные точки                                                                                        193

17. Площади и объемы                                                                                     202

18. Минимальные поверхности                                                                         226

19. Экспоненциальное отображение                                                                 236

20. Поверхности с краем                                                                                   257

21. Теорема Гаусса—Бонне                                                                              276

22. Движения и конгруэнтность                                                                        306

23. Изометрии                                                                                                  320

24. Римановы метрики                                                                                      336

Библиография                                                                                                   354

Предметный указатель                                                                                     356