Heat kernel asymptotics for quaternionic contact manifolds

In this paper, we study the heat kernel associated to the intrinsic sublaplacian on a quaternionic contact manifold considered as a subriemannian manifold. More precisely, we explicitly compute the first two coefficients \(c_0\) and \(c_1\) appearing in the small time asymptotics expansion of the heat kernel on the diagonal. We show that the second coefficient \(c_1\) depends linearly on the qc scalar curvature \(\kappa\). Finally we apply our results to compact qc-Einstein manifolds and prove the spectral invariance of geometric quantities in the subriemannian setting.