# The subelliptic heat kernel of the octonionic Hopf fibration

## TL;DR

This paper derives explicit formulas for the heat kernel and Green function of the sub-Laplacian on the 15-dimensional sphere related to the octonionic Hopf fibration, revealing spectral and geometric properties.

## Contribution

It provides the first explicit formulas for the heat kernel and Green function of the sub-Laplacian in this octonionic setting, including spectrum and distance computations.

## Key findings

- Explicit heat kernel formulas derived
- Spectrum of the sub-Laplacian obtained
- Sub-Riemannian distance explicitly computed

## Abstract

We study the sub-Laplacian of the $15$-dimensional unit sphere which is obtained by lifting with respect to the Hopf fibration the Laplacian of the octonionic projective space. We obtain in particular explicit formulas for its heat kernel and deduce an expression for the Green function of a related sub-Laplacian. As a byproduct we also obtain the spectrum of the sub-Laplacian, the small-time asymptotics of the heat kernel and explicitly compute the sub-Riemannian distance.