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Modern Geometry: Methods and Applications: The Geometry of Surfaces, Transformation Groups, and Fields - Hardcover
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.
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Language Notes
Text: English (translation)
Original Language: Russian
"About this title" may belong to another edition of this title.
- PublisherSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Publication date1984
- ISBN 10 3540908722
- ISBN 13 9783540908722
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages464
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