Champs de vecteurs holomorphes tangents aux hypersurfaces polynômiales rigides de ? 2
DOI:
https://doi.org/10.22199/S07160917.1999.0001.00008Abstract
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 ?1, ?2 in C 2, more precisely we prove that, if b?1 is strictely pseudo-convexe and not spheric in at less one point, then such map is of the form (?? + f1 (z), f2(z)), where ? ? R* and f1, f2 are two polynômes.
References
[1] F .Berteloot., Attraction des clisques analytiques et continuité holdérienne d'applications holomorphes propes, Banach Center Publications, Vol. 31, pp. 91- 98, (1995).
[2] A.Chaouech., Auto-applications holomorphes propres des domaines polynomiaux rigides de ? 2 . Publicacions Matematiqués. Vol. 40. N1, pp. 41-66, (1996).
[3] B. Coupet and S.Pinchuk., Holomorphic equivalence problem for weighted homogeneous rigid domains in ? n+1 , Indiana University Math . .Journal, to appear.
[4] K.Oeljeklaus., On the automorphism group of certain hyperbolic domains in ? 2 , Astérisque 217, pp. 193-216, (1993).
[5] N. Stanton., Infinitesimal CR automorphisms of rigid hypersurfaces in ?2, Journal of Geometric analysis, vol.1, N.3, pp. 231-267, (1991).
[2] A.Chaouech., Auto-applications holomorphes propres des domaines polynomiaux rigides de ? 2 . Publicacions Matematiqués. Vol. 40. N1, pp. 41-66, (1996).
[3] B. Coupet and S.Pinchuk., Holomorphic equivalence problem for weighted homogeneous rigid domains in ? n+1 , Indiana University Math . .Journal, to appear.
[4] K.Oeljeklaus., On the automorphism group of certain hyperbolic domains in ? 2 , Astérisque 217, pp. 193-216, (1993).
[5] N. Stanton., Infinitesimal CR automorphisms of rigid hypersurfaces in ?2, Journal of Geometric analysis, vol.1, N.3, pp. 231-267, (1991).
Published
2018-04-04
How to Cite
[1]
A. Chaouech, “Champs de vecteurs holomorphes tangents aux hypersurfaces polynômiales rigides de ? 2”, Proyecciones (Antofagasta, On line), vol. 18, no. 1, pp. 107-126, Apr. 2018.
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