Modern Geometry- Methods and Applications: Part II: The Geometry and Topology of Manifolds

B. A. Dubrovin

ISBN 10: 0387961623 / ISBN 13: 9780387961620

Edité par Springer-Verlag New York Inc., 1985

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Détails bibliographiques

• Titre: Modern Geometry- Methods and Applications: Part II: The Geometry and Topology of Manifolds
• Éditeur: Springer-Verlag New York Inc.
• Date de parution: 1985
• Langue: anglais
• ISBN à 10 chiffres: 0387961623
• ISBN à 13 chiffres: 9780387961620
• Reliure: Hardback
• État de l'article: New

A propos de ce titre

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.

Présentation de l'éditeur

This is the first volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised.