The subelliptic heat kernels of the quaternionic Hopf fibration

TL;DR

This paper investigates the sub-Laplacian on the unit sphere related to the quaternionic Hopf fibration, providing explicit heat kernel formulas, Green function expressions, and small-time asymptotics, advancing understanding of quaternionic geometric analysis.

Contribution

It offers explicit formulas for the heat kernel and Green function of the sub-Laplacian in the quaternionic setting, which were previously unknown.

Findings

Explicit heat kernel formulas derived

Green function expressions obtained

Small-time asymptotics analyzed

Abstract

The main goal of this work is to study the sub-Laplacian of the unit sphere which is obtained by lifting with respect to the Hopf fibration the Laplacian of the quaternionic projective space. We obtain in particular explicit formulas for its heat kernel and deduce an expression for the Green function of the conformal sub-Laplacian and small-time asymptotics. As a byproduct of our study we also obtain several results related to the sub-Laplacian of a projected Hopf fibration.