Moduli of Sub-Laplacians on the second Heisenberg group

TL;DR

This paper classifies sub-Laplacians on the second Heisenberg group up to contact equivalence, revealing a parameterization by positive real numbers, which advances understanding of their geometric and analytical properties.

Contribution

It provides a complete solution to the contact equivalence problem for generalized sub-Laplacians on ^2, establishing a parameterization by ^+.

Findings

Sub-Laplacians on ^2 are classified up to contact equivalence.

The family of sub-Laplacians is parameterized by ^+.

The classification simplifies the understanding of sub-Laplacian structures on ^2.

Abstract

We solve the contact equivalence problem for generalised sub-Laplacians on $\He^2$ and show that the family of sub-Laplacians on $\He^2$ modulo contact equivalence, is parameterised by $\R^+$