An Application of Stochastic Flows to Riemannian Foliations
Mason, Alan Gregory
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https://hdl.handle.net/2142/86951
Description
Title
An Application of Stochastic Flows to Riemannian Foliations
Author(s)
Mason, Alan Gregory
Issue Date
1997
Doctoral Committee Chair(s)
P. Tondeur
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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