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University of Illinois at Urbana-Champaign
An Application of Stochastic Flows to Riemannian Foliations
Abstract
dc:descriptionA 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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Mason, Alan Gregory
- Contributors dc:contributor
-
- P. Tondeur
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI9812695
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86951