Foliations on Riemannian Manifolds (Universitext) by Philippe Tondeur (PDF)

Description

A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories. This is an idea that dates back to the beginning of the theory of differential equations, i.e. the seventeenth century. Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena. He emphasized the qualitative nature of these phenomena, thereby giving strong impetus to topological methods. A second approximation is the idea of a foliation as a decomposition of a manifold into submanifolds, all being of the same dimension. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded. This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations for a proper modeling. The global study of foliations in the spirit of Poincare was begun only in the 1940’s, by Ehresmann and Reeb.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Very solid, intelligible presentation. A lot of beautiful intuitions. Can combine with other more topological references on foliations. Require some background on Riemannian geometry, like connection, curvature, etc. Very readable and highly recommended to people interested in geometric aspects of foliations.

⭐

⭐

Keywords

Free Download Foliations on Riemannian Manifolds (Universitext) in PDF format
Foliations on Riemannian Manifolds (Universitext) PDF Free Download
Download Foliations on Riemannian Manifolds (Universitext) 1988 PDF Free
Foliations on Riemannian Manifolds (Universitext) 1988 PDF Free Download
Download Foliations on Riemannian Manifolds (Universitext) PDF
Free Download Ebook Foliations on Riemannian Manifolds (Universitext)