Modern Geometry― Methods and Applications

Part II: The Geometry and Topology of Manifolds

By B.A. Dubrovin, A.T. Fomenko

1985

First Published

4.00

Average Rating

447

Number of Pages

13H34M

Audio Length

Part of Series

Graduate Texts in Mathematics book cover 1

Graduate Texts in Mathematics

Series · 240 books

By Paul Malliavin, Daniel W. Stroock, John G. Kemeny, and more

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.

Avg Rating

4.00

Number of Ratings

5 STARS

4 STARS

100%

3 STARS

2 STARS

1 STARS

goodreads

Authors

Anatoly Timofeevich Fomenko is a full Member (Academician) of the Russian Academy of Sciences, Full Member of the International Higher Education Academy of Sciences,Doctor of Physics and Mathematics, Professor, Head of the Moscow State University Section of Mathematics of the Department of Mathematics and Mechanics.Solved Plateau's Problem from the theory of minimal spectral surfaces. Author of the theory of invariants and topological classification of integrable Hamiltonian dynamic systems. Author of 200 scientific publications, 28 monographs and textbooks on mathematics, a specialist in geometry and topology, calculus of variations, symplectic topology, Hamiltonian geometry and mechanics, computer geometry. Author of a number of books on the development of new empirico-statistical methods and their application to the analysis of historical chronicles as well as the chornology of antiquity and the Middle Ages. Many Russian scientists do not accept the "New Chronology" declaring it pseudoscientific, yet no mathematical calculations on which the New Chronology is based have been proved wrong. The supporters of the New Chronology include Garry Kasparov, a former chess champion, whom many consider the greatest chess player of all time.