In this Note, we announce the result that if M is a Kahler-Einstein manifol
d with positive scalar curvature, if the initial metric has nonnegative bis
ectional curvature, and the curvature is positive somewhere, then the Kahle
r-Ricci flow converges to a Kahler-Einstein metric with constant bisectiona
l curvature. (C) 2001 Academie des sciences/Editions scientifiques et medic
ales Elsevier SAS.