Riemannian Foliations is popular PDF and ePub book, written by Molino in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Riemannian Foliations can be Read Online from any device for your convenience.
Riemannian Foliations Book PDF Summary
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.
Detail Book of Riemannian Foliations PDF
- Author : Molino
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9781468486704
- Genre : Mathematics
- Total Page : 348 pages
- Language : English
- PDF File Size : 20,5 Mb
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