Complete vector fields on
Author:
Erik Andersén
Journal:
Proc. Amer. Math. Soc. 128 (2000), 1079-1085
MSC (1991):
Primary 32M05; Secondary 34A20, 30D35
DOI:
https://doi.org/10.1090/S0002-9939-99-05123-0
Published electronically:
July 28, 1999
MathSciNet review:
1641696
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Abstract | References | Similar Articles | Additional Information
Abstract: We prove necessary and sufficient conditions for a rational vector field on to be complete.
- [AL92] Erik Andersén and László Lempert, On the group of holomorphic automorphisms of 𝐶ⁿ, Invent. Math. 110 (1992), no. 2, 371–388. MR 1185588, https://doi.org/10.1007/BF01231337
- [And90] Erik Andersén, Volume-preserving automorphisms of 𝐶ⁿ, Complex Variables Theory Appl. 14 (1990), no. 1-4, 223–235. MR 1048723, https://doi.org/10.1080/17476939008814422
- [Blo26] A. Bloch. Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires. Ann. Sci. École Norm. Sup., 43:309-362, 1926.
- [Bor97] E. Borel. Sur les zéros des fonctions entières. Acta Math., 20:357-397, 1897.
- [For96] Franc Forstneric, Actions of (𝐑,+) and (𝐂,+) on complex manifolds, Math. Z. 223 (1996), no. 1, 123–153. MR 1408866, https://doi.org/10.1007/PL00004552
- [Gre77] Mark L. Green, The hyperbolicity of the complement of 2𝑛+1 hyperplanes in general position in 𝑃_{𝑛} and related results, Proc. Amer. Math. Soc. 66 (1977), no. 1, 109–113. MR 457790, https://doi.org/10.1090/S0002-9939-1977-0457790-9
- [Kob70] Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
- [Lan87] Serge Lang, Introduction to complex hyperbolic spaces, Springer-Verlag, New York, 1987. MR 886677
- [Nis86] Yasuichiro Nishimura, Applications holomorphes injectives à jacobien constant de deux variables, J. Math. Kyoto Univ. 26 (1986), no. 4, 697–709 (French). MR 864471, https://doi.org/10.1215/kjm/1250520836
- [Nis92] Yasuichiro Nishimura, Analytic automorphisms of 𝐶² which preserve the coordinate axes, The Madison Symposium on Complex Analysis (Madison, WI, 1991) Contemp. Math., vol. 137, Amer. Math. Soc., Providence, RI, 1992, pp. 351–365. MR 1190996, https://doi.org/10.1090/conm/137/1190996
- [Pes56]
Ernst Peschl. Automorphismes holomorphes de l'espace à
dimensions complexes. C. R. Acad. Sci. Paris, 242:1836-1838, 1956. MR 17:1195f
- [RR88] Jean-Pierre Rosay and Walter Rudin, Holomorphic maps from 𝐶ⁿ to 𝐶ⁿ, Trans. Amer. Math. Soc. 310 (1988), no. 1, 47–86. MR 929658, https://doi.org/10.1090/S0002-9947-1988-0929658-4
- [Suz77] Masakazu Suzuki, Sur les opérations holomorphes du groupe additif complexe sur l’espace de deux variables complexes, Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 4, 517–546 (French). MR 590938
- [Suz78] Masakazu Suzuki, Sur les opérations holomorphes de 𝐶 et de 𝐶* sur un espace de Stein, Fonctions de plusieurs variables complexes, III (Sém. François Norguet, 1975–1977) Lecture Notes in Math., vol. 670, Springer, Berlin, 1978, pp. 80–88, 394 (French). MR 521914
- [Var] Dror Varolin. The density property for complex manifolds and geometric structures. Manuscript.
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Additional Information
Erik Andersén
Address at time of publication:
Department of Mathematics, University of Wisconsin-Madison, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53705
Email:
andersen@math.purdue.edu
DOI:
https://doi.org/10.1090/S0002-9939-99-05123-0
Received by editor(s):
May 29, 1998
Published electronically:
July 28, 1999
Additional Notes:
This work was supported by a grant from STINT
Communicated by:
Steven R. Bell
Article copyright:
© Copyright 2000
American Mathematical Society