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Titlebook: Riemannian Foliations; Pierre Molino Book 1988 Springer Science+Business Media New York 1988 Division.Finite.Isometrie.Partition.Riemannia

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發(fā)表于 2025-3-21 18:19:12 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Riemannian Foliations
編輯Pierre Molino
視頻videohttp://file.papertrans.cn/831/830303/830303.mp4
叢書名稱Progress in Mathematics
圖書封面Titlebook: Riemannian Foliations;  Pierre Molino Book 1988 Springer Science+Business Media New York 1988 Division.Finite.Isometrie.Partition.Riemannia
描述Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X ; if this vector field has no singularities, then its trajectories form a par- tition of M into curves, i.e. a foliation of codimension n - 1. More generally, a foliation F of codimension q on M corresponds to a partition of M into immersed submanifolds [the leaves] of dimension ,--------,- - . - -- p = n - q. The first global image that comes to mind is 1--------;- - - - - - that of a stack of "plaques". 1---------;- - - - - - Viewed laterally [transver- 1--------1- - - -- sally], the leaves of such a 1--------1 - - - - -. stacking are the points of a 1--------1--- ----. quotient manifold W of di- L..... -‘ _ mension q. -----~) W M Actually, this image corresponds to an elementary type of folia- tion, that one says is "simple". For an arbitrary foliation, it is only l- u L ally [on a "simpIe" open set U] that the foliation appears as a stack of plaques and admits a local quotient manifold. Globally, a leaf L may - - return and cut a simple open set U in several plaques, sometime
出版日期Book 1988
關(guān)鍵詞Division; Finite; Isometrie; Partition; Riemannian geometry; Vector field; differential equation; equation;
版次1
doihttps://doi.org/10.1007/978-1-4684-8670-4
isbn_softcover978-1-4684-8672-8
isbn_ebook978-1-4684-8670-4Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightSpringer Science+Business Media New York 1988
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gefunden. Sogar in sprichw?rtlichen Redewendungen sind seine Bestandteile pr?sent: ?Das ist ja hanebüchen“ leitet sich von der Hainbuche ab, die ein recht stabiles Holz entwickelt, und wenn jemand knallharten Unsinn redet, ist dieses spezielle Attribut auf jeden Fall angesagt. Der Wald berührt viele
板凳
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地板
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5#
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Book 1988e of folia- tion, that one says is "simple". For an arbitrary foliation, it is only l- u L ally [on a "simpIe" open set U] that the foliation appears as a stack of plaques and admits a local quotient manifold. Globally, a leaf L may - - return and cut a simple open set U in several plaques, sometime
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0743-1643 n appears as a stack of plaques and admits a local quotient manifold. Globally, a leaf L may - - return and cut a simple open set U in several plaques, sometime978-1-4684-8672-8978-1-4684-8670-4Series ISSN 0743-1643 Series E-ISSN 2296-505X
7#
發(fā)表于 2025-3-22 18:37:48 | 只看該作者
Basic Properties of Riemannian Foliations,We begin be recalling some basic results on Riemannian geometry ; for the proofs, the reader is referred to Kobayashi-Nomizu [Ko-No] or Dieudonné [Di], for example.
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The Structure of Riemannian Foliations,In this chapter we return to Riemannian foliations on compact manifolds. The results of the previous chapters enable us to describe the lifted foliation in the orthonormal transverse frame bundle. It then remains to drop down to the base by taking the quotient by the action of the structure group.
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