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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


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