International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 1, Pages 33-42
On the projections of Laplacians under Riemannian submersions
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
Received 31 December 1998
Copyright © 2001 Huiling Le. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We give a condition on Riemannian submersions from a Riemannian
manifold to a Riemannian manifold which will ensure that it
induces a differential operator on from the Laplace-Beltrami
operator on . Equivalently, this condition ensures that a
Riemannian submersion maps Brownian motion to a diffusion.