Modern geometry : methods and applications. Part I, The geometry of surfaces, transformation groups, and fields / B. A. Dubrovin, A. T. Fomenko, [and] S. P. Novikov ; translated by Robert G. Burns.
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 inste...
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Full Text (via Springer) |
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| Main Authors: | , , |
| Other Authors: | |
| Other title: | Sovremennai︠a︡ geometrii︠a︡. English. Geometry of surfaces, transformation groups, and fields. |
| Format: | eBook |
| Language: | English Russian |
| Published: |
New York, NY :
Springer-Verlag,
1984.
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| Series: | Graduate texts in mathematics ;
93. |
| Subjects: |
| Summary: | 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 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, 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. 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 terminology acceptable to physicists. |
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| Physical Description: | 1 online resource (xv, 464 pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages [455]-457) and index. |
| ISBN: | 9781468499469 1468499467 9781468499483 1468499483 |
| ISSN: | 0072-5285 ; |