## Files in this item

FilesDescriptionFormat

application/pdf

9812695.pdf (3MB)
(no description provided)PDF

## Description

 Title: An Application of Stochastic Flows to Riemannian Foliations Author(s): Mason, Alan Gregory Doctoral Committee Chair(s): P. Tondeur Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: A stochastic flow is constructed on a frame bundle adapted to a Riemannian foliation on a compact manifold. The generator A of the resulting transition semigroup is shown to preserve the basic functions and forms, and there is an essentially unique strictly positive smooth function $\phi$ satisfying A*$\phi$ = 0. This function is considered in the light of recent results of Dominguez, and an application of the ergodic theorem shows that there exists a bundle-like metric for which the mean curvature is both basic and basic-harmonic. Issue Date: 1997 Type: Text Language: English Description: 65 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997. URI: http://hdl.handle.net/2142/86951 Other Identifier(s): (MiAaPQ)AAI9812695 Date Available in IDEALS: 2015-09-28 Date Deposited: 1997
﻿