Geodesic
Effective Actions of the Unitary Group on Complex Manifolds
Canadian journal of mathematics, Tome 54 (2002) no. 6, pp. 1254-1279

Voir la notice de l'article provenant de la source Cambridge University Press

We classify all connected $n$ -dimensional complex manifolds admitting effective actions of the unitary group ${{U}_{n}}$ by biholomorphic transformations. One consequence of this classification is a characterization of ${{\mathbb{C}}^{n}}$ by its automorphism group.
DOI : 10.4153/CJM-2002-048-2
Mots-clés : 32Q57, 32M17, complex manifolds, group actions 
Isaev, A. V.; Kruzhilin, N. G. Effective Actions of the Unitary Group on Complex Manifolds. Canadian journal of mathematics, Tome 54 (2002) no. 6, pp. 1254-1279. doi: 10.4153/CJM-2002-048-2
@article{10_4153_CJM_2002_048_2,
     author = {Isaev, A. V. and Kruzhilin, N. G.},
     title = {Effective {Actions} of the {Unitary} {Group} on {Complex} {Manifolds}},
     journal = {Canadian journal of mathematics},
     pages = {1254--1279},
     year = {2002},
     volume = {54},
     number = {6},
     doi = {10.4153/CJM-2002-048-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2002-048-2/}
}
TY  - JOUR
AU  - Isaev, A. V.
AU  - Kruzhilin, N. G.
TI  - Effective Actions of the Unitary Group on Complex Manifolds
JO  - Canadian journal of mathematics
PY  - 2002
SP  - 1254
EP  - 1279
VL  - 54
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2002-048-2/
DO  - 10.4153/CJM-2002-048-2
ID  - 10_4153_CJM_2002_048_2
ER  - 
%0 Journal Article
%A Isaev, A. V.
%A Kruzhilin, N. G.
%T Effective Actions of the Unitary Group on Complex Manifolds
%J Canadian journal of mathematics
%D 2002
%P 1254-1279
%V 54
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2002-048-2/
%R 10.4153/CJM-2002-048-2
%F 10_4153_CJM_2002_048_2

[A1] [A1] Akhiezer, D. N., On the homotopy classification of complex homogeneous spaces (translated from Russian). Trans. Moscow Math. Soc. 35 (1979), 1–19. Google Scholar

[A2] [A2] Akhiezer, D. N., Homogeneous complex manifolds (translated from Russian). Encyclopaedia Math. Sci. 10, Several Complex Variables IV, 1990, 195–244, Springer-Verlag. Google Scholar

[AL] [AL] Andersen, E. and Lempert, L., On the group of holomorphic automorphisms of C . Invent.Math. 110 (1992), 371–388. Google Scholar

[GG] [GG] Goto, M. and Grosshans, F., Semisimple Lie Algebras. Marcel Dekker, 1978. Google Scholar

[H] [H] Hochschild, G., The Structure of Lie groups. Holden-Day, 1965. Google Scholar

[IKra] [IKra] Isaev, A. V. and Krantz, S. G., On the automorphism groups of hyperbolic manifolds. J. Reine Angew.Math. 534 (2001), 187–194. Google Scholar

[K] [K] Kaup, W., Reelle Transformationsgruppen und invariante Metriken auf komplexen Räumen. Invent.Math. 3 (1967), 43–70. Google Scholar

[R] [R] Rossi, H., Attaching analytic spaces to an analytic space along a pseudoconcave boundary. Proc. Conf. Complex Analysis, Minneapolis, 1964, Springer-Verlag, 1965, 242–256. Google Scholar

[VO] [VO] Vinberg, E. and Onishchik, A., Lie Groups and Algebraic Groups. Springer-Verlag, 1990. Google Scholar

Cité par Sources :