The Subelliptic Heat Kernel on the CR sphere

Abstract

We study the heat kernel of the sub-Laplacian L on the CR sphere S2n+1. An explicit and geometrically meaningful formula for the heat kernel is obtained. As a by-product we recover in a simple way the Green function of the conformal sub- Laplacian -L + n2 that was obtained by Geller [12], and also get an explicit formula for the sub-Riemannian distance. The key point is to work in a set of coordinates that reflects the symmetries coming from the fibration S2n+1 \rightarrow CPn.