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Modern Geometry- Methods and Applications

Name: Modern Geometry- Methods and Applications
Brand: Springer-Verlag New York Inc.
SKU: 01384585
Price: 61.99 EUR
Availability: InStock
Author: B.A. Dubrovin
ISBN: 9780387961620

Part II: The Geometry and Topology of Manifolds

Langue

Anglais

Livre Livre relié

Code Libristo: 01384585

Éditeurs Springer-Verlag New York Inc.

Up until recently, Riemannian geometry and basic topology were not included, even by departments or... Description détaillée

Code Libristo: 01384585

152 b

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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.