On the absence of log terms in the constant curvature case

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.