In this post we will see the book Problems in Differential Geometry and Topology by A. S. Mishchenko, Yu. P. Solovyev and A. T. Fomenko
This problem book is compiled by eminent Moscow university teachers.
Based on many years of teaching experience at the mechanics-and-mathematics department, it contains problems practically for all sections of the differential geometry and topology course delivered for university students: besides classical branches of the theory of curves and surfaces, the reader win be offered problems in smooth manifold theory, Riemannian geometry, vector fields and differential forms, general topology, homotopy theory and elements of variational calculus. The structure of the volume corresponds to A Course of Differential Geometry and Topology (Moscow University Press 1980) by Prof. A. T. Fomenko and Prof. A. S. Mishchenko Some problems however, touch upon topics outside the course lectures. The corresponding sections are provided with all necessary theoretical foundations.
About the authors
Alexander Sergeevich Mishchenko, D.Sc. (Phys.-Math.), is a professor at Moscow State University. His doctoral dissertation was devoted to modern aspects of algebraic K-theory. The author of more than 50 scientific papers and 4 books, Professor Mishchenko is a regular invited speaker at the International Congress of Mathematicians. He is a member of the Inspection Committee of the Moscow Mathematical Society.
Anatoly Timofeevich Fomenko, D.Sc. (Phys.-Math.), is a professor at Moscow State University. In his dissertation “Multidimensional Problem of Plateau on Riemannian Manifolds”, which was awarded a prize by the Moscow Mathematical Society, he solved the classical problem of variational calculus. He is a regular invited speaker at the International Congress of Mathematicians. Professor Fomenko has published more than 70 scientific papers and 5 books. His book Modern Geometry, coauthored with Academician S. R Novikov and B. A. Dubrovin, was published in French by Mir Publishers.
Yury Petrovich Solovyev, Cand.Sc. (Phys.-Math.), is a senior scientific worker at Moscow State University. Solovyev’s scientific interests lie in the field of algebraic K .. theory. He has published more than 40 papers, and serves as deputy editor-in-chief of the popular mathematics magazine Quantum.
The book was translated from the Russian by Oleg Efimov and was first published by Mir in 1985.
Credits to the original uploader for the scans.
The original copy was cleaned at bit, ocred, bookmarked and cover added.
PDF | OCR | Bookmarked | Cover | 6.2 MB | 209 pages
You can get the book here.
1. Application of Linear Algebra to Geometry 7
2. Systems of Coordinates 9
3. Riemannian Metric 14
4. Theory of Curves 16
5. Surfaces 34
6. Manifolds 53
7. Transformation Groups 60
8. Vector Fields 64
9. Tensor Analysis 70
10. Differential Forms, Integral Formulae, De Rham Cohomology 75
11. General Topology 81
12. Homotopy Theory 87
13. Covering Maps, Fibre Spaces, Riemann Surfaces 97
14. Degree of Mapping 105
15. Simplest Variational Problems 108
Answers and Hints 113