Selected problems in differential geometry and topology. Transl. from the Russian (Q2865152)

This is the English edition of a textbook, a volume of problems and practical exercises associated to the short course in differential geometry and topology for students in mathematics and physics and is based on seminars conducted by the authors at the Faculty of Mechanics and Mathematics of Moscow State University. The book has two parts. Part 1 contains problems on the standard sections of differential geometry and topology. It includes topics on: theory of curves, theory of surfaces, manifolds, tensors, differential forms and de Rham cohomologies, homotopy, degree of mapping and index of vector field. Part 2 contains additional problems on the subjects reflected in the first part and problems on new subjects intended for a more profound and advanced level of modern geometry. Next, the following topics are presented: Riemannian geometry, classical metrics on sphere, Lobachevski plane, manifolds (including elements on fibrations, phase spaces and configuration spaces), Lie groups and algebras (small Lie groups and their parameterizations used in mechanics, Lie connectivities), differential forms (de Rham integration, de Rham theory), connectivities and parallel translation, geodesics, curvature tensor, elements of algebraic topology.NEWLINENEWLINENEWLINEThere are answers and solutions given to the problems presented in the book.NEWLINENEWLINENEWLINEThe text is presented in an accessible form, supplemented by a large number of drawings. It also contains useful references for postgraduates and researchers specializing in modern geometry and its applications.