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On the projections of Laplacians under Riemannian submersions

International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 1, Page 33-42, 2001., 2001
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.
Huiling Le
wiley   +1 more source