Equivalence of sub-Laplacian on Polarized groups

Abstract

We characterize smooth maps between sub-Riemannian Lie groups that commute with sub-Laplacians. We show they are sub-Riemannian conformal submersions. Our work clarifies the analysis initiated on Carnot groups in \cite{MR2363343}. In particular, we show that the sub-Laplacian in a Carnot group determines the sub-Riemannian structure.

arXiv comment19 pages. Fixed formula in Theorem A; extended results to the case lambda=0