An Application of Stochastic Flows to Riemannian Foliations

Details An Application of Stochastic Flows to Riemannian Foliations An Application of Stochastic Flows to Riemannian Foliations

1998-12-18

arxiv.org/abs/math/9812117v10

Mathematics

Differential Geometry

LaTex, 36 pages, no figures. To appear in Houston Journal of Mathematics

Scientific paper

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 used to perturb the metric, and an application of the ergodic theorem shows that there exists a bundle-like metric for which the basic projection of the mean curvature is basic-harmonic.

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