Equivalence of sub-Laplacian on Polarized groups

Published 31 Dec 2024 in math.DG and math.AP | (2501.00576v1)

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.

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