Comptes Rendus
no. 7
Complex analysis/Analytic geometry
On the Lie group structure of automorphism groups

Presented by: Jean-Pierre Demailly

Yoshikazu Nagata1
1 Department of Mathematics and The SRC-GAIA, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea
Comptes Rendus. Mathématique, Volume 355 (2017) no. 7, pp. 769-773.

We give a sufficient condition for complex manifolds for automorphism groups to become Lie groups. As an application, we see that the automorphism group of any strictly pseudoconvex domain or finite-type pseudoconvex domain has a Lie group structure.

Nous donnons une condition suffisante pour que le groupe des automorphismes d'une variété complexe possède une structure de groupe de Lie. Comme application, nous obtenons que le groupe des automorphismes de tout domaine strictement pseudo-convexe ou de type pseudo-convexe fini a une structure de groupe de Lie.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.06.007

Yoshikazu Nagata 1

1 Department of Mathematics and The SRC-GAIA, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea 
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Yoshikazu Nagata. On the Lie group structure of automorphism groups. Comptes Rendus. Mathématique, Volume 355 (2017) no. 7, pp. 769-773. doi : 10.1016/j.crma.2017.06.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.06.007/

[1] E. Bishop Mappings of partially analytic spaces, Amer. J. Math., Volume 83 (1961), pp. 209-242

[2] B.Y. Chen; J.H. Zhang The Bergman metric on a Stein manifold with a bounded plurisubharmonic function, Trans. Amer. Math. Soc., Volume 354 (2002) no. 8, pp. 2997-3009

[3] A.-K. Gallagher; T. Harz; G. Herbort On the dimension of the Bergman space for some unbounded domains, J. Geom. Anal., Volume 27 (2017) no. 2, pp. 1435-1444

[4] A. Huckleberry; A. Isaev Infinite-dimensionality of the automorphism groups of homogeneous Stein manifolds, Math. Ann., Volume 344 (2009) no. 2, pp. 279-291

[5] S. Kobayashi Geometry of bounded domains, Trans. Amer. Math. Soc., Volume 92 (1959), pp. 267-290

[6] S. Kobayashi Transformation Groups in Differential Geometry, Springer-Verlag, Berlin, 1995

[7] R. Narasimhan Holomorphically complete complex spaces, Amer. J. Math., Volume 82 (1961), pp. 917-934

[8] R. Narasimhan Several Complex Variables, The University of Chicago Press, 1971

[9] T. Ohsawa On complete Kähler domains with C1-boundary, Publ. Res. Inst. Math. Sci., Volume 16 (1980) no. 3, pp. 929-940

[10] P. Pflug; W. Zwonek Lh2-functions in unbounded balanced domains | arXiv

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