In this post we will see A Course of Differential Geometry and Topology – A. Mishchenko and A. Fomenko. Earlier we had seen the *Problem Book on Differential Geometry and Topology* by these two authors which is the associated problem book for this course.

About the book

The present course deals with the fundamentals of differential geometry and topology whose present state is the culmination of contributions of generations of mathematicians.

The English edition has been thoroughly revised in line with comments and suggestions, made by our readers, the mistakes and misprints that were detected have been corrected. This is essentially a textbook for 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 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 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* which was specially compiled to accompany this course.

The book was translated from the Russian by *Anatoly Talshev* and was first published by Mir in 1988.

PDF | 75 MB | 459 Pages | Cover |

All credits to the original uploader.

*Note*: Though the file size is large ~ 75 MB, the scan quality is poor, OCR may not be of any help.

You can get the book here (libgen link) and here (IA link)

## Contents

Preface to English Edition 8

Preface to Russian Edition 9

Chapter 1 Introduction to Differential Geometry 12

Chapter 2 General Topology 67

Chapter3 Smooth Manifolds (General theory) 92

Chapter 4 Smooth Manifolds (Examples) 147

Chapter 5 Tensor Analysis and Riemannian Geometry 294

Chapter 6 Homology Theory 371

Chapter 7 Simple Variational Problems in Riemannian Geometry 407