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Titlebook: Differential Geometry of Foliations; The Fundamental Inte Bruce L. Reinhart Book 1983 Springer-Verlag Berlin Heidelberg 1983 Blätterung (Ma

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书目名称Differential Geometry of Foliations
副标题The Fundamental Inte
编辑Bruce L. Reinhart
视频videohttp://file.papertrans.cn/279/278765/278765.mp4
丛书名称Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
图书封面Titlebook: Differential Geometry of Foliations; The Fundamental Inte Bruce L. Reinhart Book 1983 Springer-Verlag Berlin Heidelberg 1983 Blätterung (Ma
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
doihttps://doi.org/10.1007/978-3-642-69015-0
isbn_softcover978-3-642-69017-4
isbn_ebook978-3-642-69015-0
copyrightSpringer-Verlag Berlin Heidelberg 1983
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发表于 2025-3-21 23:44:32 | 显示全部楼层
d 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 o
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On Relativity, Relativism, and Social Theoryference among orders of differentiability is of increasing geometric significance. Finally, some concepts of particular usefulness in foliation theory are studied and a variety of examples given as motivation for later chapters.
发表于 2025-3-22 06:30:59 | 显示全部楼层
Differential Geometric Structures and Integrability,ference among orders of differentiability is of increasing geometric significance. Finally, some concepts of particular usefulness in foliation theory are studied and a variety of examples given as motivation for later chapters.
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On Relativity, Relativism, and Social Theorys, the first step is to introduce various approaches to the definition of a structure, and show how the principal examples, especially foliations, fit in. Next, since a foliation can be viewed as an integrable reduction of the group of the tangent bandle, some general facts about integrability are i
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