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Geometry IV : Non-regular Riemannian Geometry /
This volume of the Encyclopaedia contains two articles, which give a survey of modern research into non-regular Riemannian geometry, carried out mostly by Russian mathematicians. The first article written by Reshetnyak is devoted to the theory of two-dimensional Riemannian manifolds of bounded curva...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg,
1993.
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| Colección: | Encyclopaedia of mathematical sciences ;
70. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | This volume of the Encyclopaedia contains two articles, which give a survey of modern research into non-regular Riemannian geometry, carried out mostly by Russian mathematicians. The first article written by Reshetnyak is devoted to the theory of two-dimensional Riemannian manifolds of bounded curvature. Concepts of Riemannian geometry, such as the area andintegral curvature of a set, and the length and integral curvature of a curve are also defined for these manifolds. Some fundamental results of Riemannian goemetry like the Gauss-Bonnet formula are true in the more general case considered in the book. The second article by Berestovskij and Nikolaev is devoted to the theory of metric spaces whose curvature lies between two given constants. The main result is that these spaces are infact Riemannian. This result has important applications in global Riemanniangeometry. Both parts cover topics, which have not yet been treated in monograph form. Hence the book will be immensely useful to graduate students and researchers in geometry, in particular Riemannian geometry. |
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| Descripción Física: | 1 online resource (vii, 252 pages) |
| ISBN: | 9783662028971 3662028972 3540547010 9783540547013 0387547010 9780387547015 |
| ISSN: | 0938-0396 ; |