Recurrence relations for heat kernels on spheres

Abstract

In this paper, we obtain two recurrence relations of the heat kernels for spheres that are similar to the two recurrence relations of heat kernels for hyperbolic spaces in [5] by using a different method. As an application of the recurrence relations for heat kernels, we compute the diagonal of heat kernels for odd dimensional hyperbolic spaces and the heat trace asymptotic expansions for odd dimensional spheres. This provides a different approach with [13] for the computation of heat trace coefficients of odd dimensional spheres.