CONTENTS

Chapters in this book

1. Frontmatter i
2. PREFACE vii
3. CONTENTS xi
4. CHAPTER I. PRELIMINARIES 1
5. CHAPTER II. THEORY OF CURVES 17
6. CHAPTER III. CONCEPT OF A SURFACE. FIRST FUNDAMENTAL FORM. FOUNDATIONS OF TENSOR CALCULUS 72
7. CHAPTER IV. SECOND FUNDAMENTAL FORM. GAUSSIAN AND MEAN CURVATURE OF A SURFACE 118
8. CHAPTER V. GEODESIC CURVATURE AND GEODESICS 154
9. CHAPTER VI. MAPPINGS 175
10. CHAPTER VII. ABSOLUTE DIFFERENTIATION AND PARALLEL DISPLACEMENT 219
11. CHAPTER VIII. SPECIAL SURFACES 243
12. SUPPLEMENTARY PROBLEMS 301
13. ANSWERS TO PROBLEMS 320
14. ANSWERS TO ODD-NUMBERED SUPPLEMENTARY PROBLEMS 347
15. COLLECTION OF FORMULAE 353
16. BIBLIOGRAPHY 368
17. INDEX 373