书目名称 | Differential Geometry of Foliations | 副标题 | The Fundamental Inte | 编辑 | Bruce L. Reinhart | 视频video | http://file.papertrans.cn/279/278765/278765.mp4 | 丛书名称 | Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge | 图书封面 |  | 描述 | Whoever you are! How can I but offer you divine leaves . . . ? Walt Whitman The object of study in modern differential geometry is a manifold with a differ ential structure, and usually some additional structure as well. Thus, one is given a topological space M and a family of homeomorphisms, called coordinate sys tems, between open subsets of the space and open subsets of a real vector space V. It is supposed that where two domains overlap, the images are related by a diffeomorphism, called a coordinate transformation, between open subsets of V. M has associated with it a tangent bundle, which is a vector bundle with fiber V and group the general linear group GL(V). The additional structures that occur include Riemannian metrics, connections, complex structures, foliations, and many more. Frequently there is associated to the structure a reduction of the group of the tangent bundle to some subgroup G of GL(V). It is particularly pleasant if one can choose the coordinate systems so that the Jacobian matrices of the coordinate transformations belong to G. A reduction to G is called a G-structure, which is called integrable (or flat) if the condition on the Jacobians is satisfied. | 出版日期 | Book 1983 | 关键词 | Blätterung (Math; ); Differentialgeometrie; Geometry; Riemannian manifold; diffeomorphism; differential ge | 版次 | 1 | doi | https://doi.org/10.1007/978-3-642-69015-0 | isbn_softcover | 978-3-642-69017-4 | isbn_ebook | 978-3-642-69015-0 | copyright | Springer-Verlag Berlin Heidelberg 1983 |
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