| 书目名称 | Foliations on Riemannian Manifolds | | 编辑 | Philippe Tondeur | | 视频video | | | 丛书名称 | Universitext | | 图书封面 |  | | 描述 | A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories. This is an idea that dates back to the beginning of the theory of differential equations, i.e. the seventeenth century. Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena. He emphasized the qualitative nature of these phenomena, thereby giving strong impetus to topological methods. A second approximation is the idea of a foliation as a decomposition of a manifold into submanifolds, all being of the same dimension. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded. This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations for a proper modeling. The global study of folia | | 出版日期 | Book 1988 | | 关键词 | Mean curvature; Riemannian geometry; curvature; manifold | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4613-8780-0 | | isbn_softcover | 978-0-387-96707-3 | | isbn_ebook | 978-1-4613-8780-0Series ISSN 0172-5939 Series E-ISSN 2191-6675 | | issn_series | 0172-5939 | | copyright | Springer-Verlag New York Inc. 1988 |
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发表于 2025-3-21 19:32:38
