Heat kernel recurrence on space forms and applications
Abstract
In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in DM. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres. Finally, as an application, we compute the diagonal of heat kernels for odd dimensional hyperbolic spaces and the heat trace asymptotic expansions for odd dimensional spheres.
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