MODERN GEOMETRY- METHODS AND APPLICATIONS by B. A. Dubrovin, A. T. Fomenko, I. S. Novikov ( 9780387961620 )

Item Details

Title:

MODERN GEOMETRY- METHODS AND APPLICATIONS
PART II: THE GEOMETRY AND TOPOLOGY OF MANIFOLDS

By:

B. A. Dubrovin, A. T. Fomenko, I. S. Novikov

Format:

Hardback

List price:	£62.99
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ISBN 10:

0387961623

ISBN 13:

9780387961620

Publisher:

SPRINGER-VERLAG NEW YORK INC.

Pub. date:

5 August, 1985

Edition:

1985 ed.

Series:

Graduate Texts in Mathematics 104

Pages:

432

Description:

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.

Synopsis:

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.

Illustrations:

XV, 432 p.

Publication:

Imprint:

Springer-Verlag New York Inc.

Returns:

Returnable

Some other items by this author:

A SHORT COURSE IN DIFFERENTIAL GEOMETRY AND TOPOLOGY (HB)

ALGORITHMIC AND COMPUTER METHODS FOR THREE-MANIFOLDS (HB)

ALGORITHMIC AND COMPUTER METHODS FOR THREE-MANIFOLDS (PB)

BASIC ELEMENTS OF DIFFERENTIAL GEOMETRY AND TOPOLOGY (HB)