The issue related to the so-called dimensional reduction procedure is revis
ited within the Euclidean formalism. First, it is shown that for symmetric
spaces, the local exact heat-kernel density is equal to the reduced one, on
ce the harmonic sum has been successfully performed. In the general case, d
ue to the impossibility to deal with exact results, the short t heat-kernel
asymptotics is considered. It is found that the exact heat-kernel and the
dimensionally reduced one coincide up to two nontrivial leading contributio
ns in the short t expansion. Implications of these results with regard to d
imensional-reduction anomaly are discussed. (C) 2001 Published by Elsevier
Science B.V.