The subelliptic heat kernel of the octonionic Hopf fibration
Abstract
We study the sub-Laplacian of the -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.
Keywords
Cite
@article{arxiv.1904.08568,
title = {The subelliptic heat kernel of the octonionic Hopf fibration},
author = {Fabrice Baudoin and Gunhee Cho},
journal= {arXiv preprint arXiv:1904.08568},
year = {2020}
}
Comments
Companion paper of arXiv:1112.3084 and of arXiv:1310.5938. The geometry is quite different but there is a natural overlap in the method of computing the heat kernel and its asymptotics once the formula for the radial part of the sub-Laplacian is obtained. v2 typos corrected and presentation improved