Heat kernel asymptotics for quaternionic contact manifolds
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2021
- DOI:
- 10.48550/arXiv.2103.00892
- arXiv:
- arXiv:2103.00892
- Bibcode:
- 2021arXiv210300892L
- Keywords:
-
- Mathematics - Differential Geometry;
- Mathematics - Analysis of PDEs;
- 53C17;
- 58J50;
- 41A60;
- 35K08
- E-Print:
- arXiv admin note: text overlap with arXiv:2102.04784