Einstein-Kahler metrics on a class of bundles involving integral weights

We prove that some compact complex bundles, defined over Pd1-1 x...x Pdn-1 (where P-d is the complex projective space of complex dimension d), and depending on n integral weights a(1) ,..., a(n), have positive first Chem class if 1 less than or equal to a(h) less than or equal to d(h) - 1 for all h, and carry Einstein-Kahler metrics when a(1) = ... = a(n) and d(1) = ... = d(n). (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.