Sub-Laplacian intertwining maps between sub-Riemannian Lie groups are conformal submersions, and on Carnot groups the sub-Laplacian determines the sub-Riemannian structure.
Riemannian submersions commuting with the Laplacian
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Equivalence of sub-Laplacian on Polarized groups
Sub-Laplacian intertwining maps between sub-Riemannian Lie groups are conformal submersions, and on Carnot groups the sub-Laplacian determines the sub-Riemannian structure.