Abstract
AbstractWe present an explicit form of the subelliptic heat kernel of the intrinsic sublaplacian $$\Delta _{\textrm{sub}}^5$$
Δ
sub
5
induced by a rank 5 trivializable subriemannian structure on the Euclidean seven dimensional sphere $$\mathbb {S}^7$$
S
7
. This completes the heat kernel analysis of trivializable subriemannian structures on $$\mathbb {S}^7$$
S
7
induced by a Clifford module action on $$\mathbb {R}^8$$
R
8
. As an application we derive the spectrum of $$\Delta _{\textrm{sub}}^5$$
Δ
sub
5
and the Green function of the conformal sublaplacian in an explicit form.
Funder
Japan Society for the Promotion of Science
Deutsche Forschungsgemeinschaft
Research Institute for Mathematical Sciences
Gottfried Wilhelm Leibniz Universität Hannover
Publisher
Springer Science and Business Media LLC