no. 4
On invariant domains in certain complex homogeneous spaces
Annales de l'Institut Fourier, Tome 47 (1997) no. 4, pp. 1101-1115

Given a compact connected Lie group K. For a relatively compact K-invariant domain D in a Stein K ℂ -homogeneous space, we prove that the automorphism group of D is compact and if K is semisimple, a proper holomorphic self mapping of D is biholomorphic.

Soit K un groupe de Lie connexe compact. Pour un domaine K, G-invariant et relativement compact dans un espace homogène de Stein K ℂ /L ℂ , nous montrons que le groupe des automorphismes de D est compact et si K est semi-simple, une application holomorphe propre de D est biholomorphe.

@article{AIF_1997__47_4_1101_0,
     author = {Zhou, Xiang-Yu},
     title = {On invariant domains in certain complex homogeneous spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {1101--1115},
     year = {1997},
     publisher = {Association des Annales de l'Institut Fourier},
     volume = {47},
     number = {4},
     doi = {10.5802/aif.1593},
     mrnumber = {99a:32045},
     zbl = {0881.32015},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.1593/}
}
TY  - JOUR
AU  - Zhou, Xiang-Yu
TI  - On invariant domains in certain complex homogeneous spaces
JO  - Annales de l'Institut Fourier
PY  - 1997
SP  - 1101
EP  - 1115
VL  - 47
IS  - 4
PB  - Association des Annales de l'Institut Fourier
UR  - https://www.numdam.org/articles/10.5802/aif.1593/
DO  - 10.5802/aif.1593
LA  - en
ID  - AIF_1997__47_4_1101_0
ER  - 
%0 Journal Article
%A Zhou, Xiang-Yu
%T On invariant domains in certain complex homogeneous spaces
%J Annales de l'Institut Fourier
%D 1997
%P 1101-1115
%V 47
%N 4
%I Association des Annales de l'Institut Fourier
%U https://www.numdam.org/articles/10.5802/aif.1593/
%R 10.5802/aif.1593
%G en
%F AIF_1997__47_4_1101_0
Zhou, Xiang-Yu. On invariant domains in certain complex homogeneous spaces. Annales de l'Institut Fourier, Tome 47 (1997) no. 4, pp. 1101-1115. doi: 10.5802/aif.1593

[1] A. Andreotti, T. Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math., 69 (1959), 713-717. | Zbl | MR

[2] H. Azad, J.-J. Loeb, Plurisubharmonic functions and the Kempf-Ness theorem, Bull. London Math. Soc., 25 (1993), 162-168. | Zbl | MR

[3] E. Bedford, Proper holomorphic mappings, Bull. Amer. Math. Soc., 10 (1984), 157-175. | Zbl | MR

[4] E. Bedford, On the automorphism group of a Stein manifold, Math. Ann., 266 (1983), 215-227. | Zbl | MR

[5] A. Borel, Symmetric compact complex spaces, Arch. Math., 33 (1979), 49-56. | Zbl | MR

[6] R. Bott, L. Tu, Differential forms in algebraic topology, Springer-Verlag, New York, Heidelberg, Berlin, 1982. | Zbl | MR

[7] G. Fels, L. Geatti, Invariant domains in complex symmetric spaces, J. reine angew. Math., 454 (1994), 97-118. | Zbl | MR

[8] F. Forstnerič, Proper holomorphic mappings. A survey, in Proceedings of the special year on several complex variables at Mittag-Leffler Institute, E. Fornaess ed., Princeton University Press, Princeton, 1993. | Zbl | MR

[9] H. Grauert, Analytische Faserungen über holomorph-vollständigen Räumen, Math. Ann., 135 (1958), 263-273. | Zbl | MR

[10] W. Greub, S. Halperin, R. Vanstone, Connections, curvature, and cohomology, Academic Press, New York, London, 1972. | MR | Zbl

[11] P. Heinzner, Geometric invariant theory on Stein space, Math. Ann., 289 (1991), 631-662. | Zbl | MR | EuDML

[12] P. Heinzner, Equivariant holomorphic extensions of real analytic manifolds, Bull. Soc. Math. France., 121 (1993), 445-463. | Numdam | Zbl | MR | EuDML

[13] P. Heinzner, A. Huckleberry, Invariant plurisubharmonic exhaustions and retractions, Manu. Math., 83 (1994), 19-29. | Zbl | MR | EuDML

[14] P. Heinzner, F. Kutzschebauch, An equivariant version of Grauert's Oka principle, Invent. Math., 119 (1995), 317-346. | Zbl | MR | EuDML

[15] M. Hirsch, Differential topology, Springer-Verlag, New York, Heidelberg, Berlin, 1976. | Zbl | MR

[16] F. Hirzebruch, Topological methods in algebraic geometry, Springer-Verlag, New York, Heidelberg, Berlin, 1966. | Zbl | MR

[17] L. Hörmander, An introduction to complex analysis in several variables, North-Holland, Amsterdam, 1966. | Zbl

[18] D. Husemoller, Fibre bundles, McGraw-Hill, New York et al., 1966. | Zbl | MR

[19] L. Kaup, B. Kaup, Holomorphic functions of several variables, Walter de Gruyter, Berlin, New York, 1983. | Zbl | MR

[20] S. Kobayashi, Intrinsic distances, measures, and geometric function theory, Bull. Amer. Math. Soc., 82 (1976), 357-416. | Zbl | MR

[21] H. Kraft, Geomtrische Methoden in der Invariantentheri, Braunschweig-Wiesbaden, Vieweg, 1985. | MR | Zbl

[22] M. Lassalle, Séries de Laurent des functions holomorphes dans la complexification d'un espace symétrique compact, Ann. Scient. Éc. Norm. Sup., 11 (1978), 167-210. | Numdam | Zbl | MR | EuDML

[23] W. Massey, A basic course in algebraic topology, Springer-Verlag, New York, Heidelberg, Berlin, 1991. | Zbl | MR

[24] J. Milnor, On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc., 90 (1959), 272-280. | Zbl | MR

[25] N. Mok, Rigiditity of holomorphic self-mappings and the automorphism groups of hyperbolic Stein spaces, Math. Ann., 266 (1984), 433-447. | Zbl | EuDML | MR

[26] R. Narasimhan, On the homology group of Stein spaces, Invent. Math., 2 (1967), 377-385. | Zbl | MR | EuDML

[27] R. Narasimhan, Several complex variables, University of Chicago, Chicago, 1971. | Zbl | MR

[28] A.L. Onishchik, Topology of transitive transformation groups, Fizmatlit Publishing Company, Moscow, 1994 (Russian). | Zbl | MR

[29] S. Pinchuk, On proper holomorphic mappings of strictly psedoconvex domains, Siberian Math. J., 15 (1974), 909-917 (Russian). | Zbl | MR

[30] R. Remmert, K. Stein, Eigentlische holomorphe Abbildungen, Math. Z., 73 (1960), 159-189. | Zbl | MR | EuDML

[31] N. Steenrod, Topology of fibre bundles, Princeton University Press, Princeton, 1951. | Zbl | MR

[32] V. Varadarajan, Lie groups, Lie algebras, and their representations, Springer-Verlag, New York, Heidelberg, Berlin, 1984. | MR | Zbl

[33] J. Wolf, Spaces of constant curvature, Publish or Perish, Boston, 1974. | Zbl | MR

[34] X.Y. Zhou, On orbit connectedness, orbit convexity, and envelopes of holomorphy, Izvestija RAN., Ser. Math., 58 (1994), 196-205. | Zbl | MR

Cité par Sources :