Riemannian Foliations: 73 (Progress in Mathematics, 73) - Image 1

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Birkhauser Riemannian Foliations: 73 (Progress in Mathematics, 73)

Name: Riemannian Foliations: 73 (Progress in Mathematics, 73)
Brand: Birkhauser
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Geometry & Topology

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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, sometimes even an infinite number of plaques.

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Brand: Birkhauser
Format: Paperback
ASIN: 1468486721
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Geometry & Topology
Domain: Amazon UK
Publication Date: 27 July 2012
Listed Since: 03 March 2013

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Birkhauser Riemannian Foliations: 73 (Progress in Mathematics, 73)

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