Problems In Differential Geometry And Topology | A. S. Mishchenko, Yu. P. Solovyev, 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.

Preface 5
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
Bibliography 208