Steinness of bundles with fiber a Reinhardt bounded domain
Résumé
Let E denote a bundle with fiber D and with basis B. Both D and B are assumed to be Stein. For D a Reinhardt bounded domain of dimension two or three: (1) We give a necessary and sufficient condition on D for the existence of a non-Stein such E (Theorem 1); (2) We give a necessary and sufficient criterion for E to be Stein (Theorem 2). For D a Reinhardt bounded domain of any dimension, we give a sufficient criterion for E to be Stein (Theorem 3).