Free download скачать Basic Elements of Differential Geometry and Topology by S. P. Novikov , A. T. Fomenko
English | PDF | 1990 | 499 Pages | ISBN : 0792310098 | 28.9 MB
For  a number  of  years, beginning with the early 70's, the authors have been delivering lectures on the fundamentals  of  geometry and topology in the Faculty  of Mechanics and Mathematics  of  Moscow State University. This text-book is the result of  this work.  We  shall recall that for a long period  of  time the basic elements  of modern geometry and topology were not included, even  by  departments and faculties of  mathematics, as compulsory subjects in a university-level mathematical education. The  standard courses in classical differential geometry have gradually become outdated, and there has been, hitherto, no unanimous standpoint  as  to  which parts  of modern geometry should be viewed as abolutely essential  to  a modern mathematical education. In view  of  the necessity  of  using a large number  of  geometric concepts and methods, a modernized course in geometry was begun  in  1971 in the Mechanics division  of  the Faculty  of  Mechanics and Mathematics  of  Moscow State University. In addition to the traditional geometry  of  curves and surfaces, the course included the fundamental priniciples  of  tensor analysis, Riemannian geometry and topology. Some time later this course was also introduced in the division  of  mathematics. On the basis  of  these lecture courses, the following text-books appeared:

S.P. Novikov: Differential Geometry, Parts I and II, Research Institute  of Mechanics  of  Moscow State University, 1972. S.P. Novikov and A.T. Fomenko: Differe
Institute  of  Mechanics  of  Moscow State University, 1974.
The  present book is the outcome  of  a revision and updating  of  the above-mentioned lecture notes. The book is intended for the mathematical, physical and  mechanical education  of  second and third year university students. The minimum abstractedness  of  the language and style  of  presentation  of  the material, consistency with the language  of  mechanics and physics, and the preference for the material important for natural sciences were the basic principles  of  the presentation.
At the end  of  the book are several Appendices which may serve to diversify the material presented in the main text. So, for the purposes  of  mechanical and physical education the information on elementary groups  of  transformations and geometric elements  of  variational calculus can be extended using these Appendices. For  mathematicians, the Appendices may serve to enrich their knowledge  of Lobachevsky geometry and homology theory. We believe that Appendices 2 and 3 are very instructive for those who wish to become acquainted with the simplest geometric ideas fundamental to physics. Appendix 7 includes selected problems and exercises for the course.
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