miércoles, 24 de agosto de 2016

The English edition has been thoroughly revised in line with comments and suggestions made by our readers, and the mistakes and misprints that were detected have been corrected. This is essentially a textbook for a modern course on differential geometry and topology, which is much wider than the traditional courses on classical differential geometry, and it covers many branches of mathematics a knowledge of which has now become essential for a modern mathematical education.

We hope that a reader who has mastered this material will be able to do independent research both in geometry and in other related fields. To gain a deeper understanding of the material of this book, we recommend the reader should solve the questions in A.S. Mishchenko, Yu.P. Solovyev, and A.T. Fomenko, Problems in Differential Geometry and Topology (Mir Publishers, Moscow, 1985) which was specially compiled to accompany this course.


Preface to the English edition
Preface to the Russian edition
Chapter 1. Introduction to differential geometry
Chapter 2. General topology
Chapter 3. Smooth manifolds (general theory)
Chapter 4. Smooth manifolds (examples)
Chapter 5. Tensor, analysis and Riemannian geometry
Chapter 6. Homology theory
Chapter 7. Simple variational problems in Riemannian geometry

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