International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 1, Pages 33-41
doi:10.1155/S0161171201003751

On the projections of Laplacians under Riemannian submersions

Abstract

We give a condition on Riemannian submersions from a Riemannian manifold M to a Riemannian manifold N which will ensure that it induces a differential operator on N from the Laplace-Beltrami operator on M. Equivalently, this condition ensures that a Riemannian submersion maps Brownian motion to a diffusion.