Abstract
In this paper, we present two works. The .first give a complet description of tangent holomorphic vector fields of rigid polynomial hypersurfaces in C2 which is not spheric at the origine.In the second we studie the propre holomorphic mappings between rigid polynomial domains Ω1, Ω2 in C 2, more precisely we prove that, if bΩ1 is strictely pseudo-convexe and not spheric in at less one point, then such map is of the form (αω + f1 (z), f2(z)), where α ∊ R* and f1, f2 are two polynomes.
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