On the absence of log terms in the constant curvature case

Article type: Research Article

Authors: Brüning, Jochen | Schröder, Herbert

Affiliations: Institut für Mathematik, Universität Augsburg, 8900 Augsburg, Fed. Rep. Germany

Abstract: The classical result of Minakshisundaram and Pleijel on the asymptotic expansion of the trace of the heat semigroup associated with the Laplacean on a compact Riemannian manifold M has been generalized by Brüning and Heintze to the case that a compact group is acting on M by isometries. They obtained an asymptotic expansion involving logarithmic terms. Here we prove that these terms vanish if M has constant sectional curvature or if M is a warped product M=[0,π]×fSn with n≥2 and suitable f.

DOI: 10.3233/ASY-1988-1302

Journal: Asymptotic Analysis, vol. 1, no. 3, pp. 193-203, 1988