| In this volume of the Encyclopaedia, the authors give a tour of the principal areas and methods of modern differential geometry. The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry Beginning at the introductory level with curves in Euclidean space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book. |
| R.V. Gamkrelidze, Academy of Sciences of the USSR, Steklov Mathematical Institute, ul. Vavilova 42, 117966 Moscow, Institute for Scientific Information (VINITI), ul. Usievicha 20a, 125219 Moscow, USSR ... .. << 查看详细 |
| preface chapter 1. introduction: a metamathematical view of differential geometry 1. algebra and geometry - the duality of the intellect 2. two examples: algebraic geometry, propositional logic and set theory 3. on the history of geometry 4. differential calculus and commutative algebra 5. what is differential geometry? chapter 2. the geometry of surfaces chapter 3. the field approach of riemann chapter 4. the group approach of lie and klein. the geometry of transformation groups chapter 5. the geometry of differential equations chapter 6. geometric structures chapter 7. the equivalence problem, differential invariants and pseudogroups chapter 8. global aspects of differential geometry commentary on the references references author index subject index |
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