We apply Painleve analysis to the Ricci-flat Einstein equations for a warpe
d product with an arbitrary number of factors. We find that, as in the situ
ation of the two factors examined [J. Geom. Phys. 38, 183-206 (2001)], the
cases when the total dimension is 10 or 11 are singled out by the analysis.
(C) 2001 American Institute of Physics.