Abstract
Let Ω be a bounded symmetric domain of type IV and dimension bigger than four. We show that a Stein manifold of the same dimension as Ω and with the same automorphism group is biholomorphic to Ω.
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Azad H., Loeb J.J.: Plurisubharmonic functions and Kählerian metrics on complexification of symmetric spaces. Indag. Math. N.S. 4(3), 365–375 (1992)
Azad H., Loeb J.J.: Plurisubharmonic functions and the Kempf-Ness theorem. Bull. Lond. Math. Soc. 25(2), 162–168 (1993)
Bröker, T., tom Diek, T.: Representations of Compact Lie Groups. In: Graduate Texts in Mathematics. Springer-Verlag, New York, (1985)
Burns D., Shnider S., Wells R.O.: Deformations of strictly pseudoconvex domains. Invent. Math. 46(3), 237–253 (1978)
Cartan H.: Les fonctions de deux variables complexes et le problème de la représentation analytique. J. Math. Pure. Appl. 10, 1–114 (1931)
Fels, G., Huckleberry, A.T., Wolf, J.A.: Cycle spaces of flag domains: a complex geometric viewpoint. In: Progress in Mathematics, vol. 245. Birkhäuser, Boston (2005)
Harvey F.R., Wells R.O.: Zero sets of non-negative strictly plurisubharmonic functions. Math. Ann. 201, 165–170 (1973)
Heinzner P.: Geometric invariant theory on Stein spaces. Math. Ann. 289, 631–662 (1991)
Helgason, S.: Differential Geometry, Lie Groups and Symmetric Spaces. Pure Appl. Math. vol. 80. Academic Press Inc., London (1978)
Huckleberry A.T., Isaev A.V.: Classical Symmetries of Complex Manifolds. J. Geom. Anal. 20(1), 132–152 (2010)
Isaev A.V.: Effective actions of the unitary group on complex manifolds. Canad. J. Math. 54(6), 1254–1279 (2002)
Isaev A.V.: Characterization of the unit ball in \({\mathbb{C}^n}\) among complex manifolds of dimension n. J. Geom. Anal. 14(4), 697–700 (2004)
Isaev A.V.: Erratum. J. Geom. Anal. 18(3), 919 (2008)
Isaev A.V.: A remark on a theorem by Kodama and Shimizu. J. Geom. Anal. 18(3), 795–799 (2008)
Kahn, R.H.: Semi-simple Lie Algebras and Their Representations. In: Dover Books in Mathematics. Dover Publications Inc., Mineola, NY, (2006)
Kobayashi S.: Transformation Groups in Differential Geometry. Springer-Verlag, Berlin (1972)
Kobayashi, S.: Hyperbolic complex spaces. In: Grundlehren der Mathematischen Wissenschaften, vol. 318. Springer-Verlag, Berlin (1998)
Kodama A., Shimizu S.: An intrinsic characterization of the unit polydisc. Mich. Math. J. 56(1), 173–181 (2008)
Lassalle, M.: Séries de Laurent des fonctions holomorphes dans la complexification d’un espace symétrique compact. Ann. Sci. Éc. Norm. Supér., Sér. II IV, 81–105 (1973)
Luna D.: Slices étale. Bull. Soc. Math. France 33, 81–105 (1973)
Palais, R.: A global formulation of the Lie theory of transformation groups. Mem. Am. Math. Soc. 22, 1955
Vladimirov V.S.: Methods of the theory of functions of many complex variables. Dover Publications Inc., Mineola, New York (2007)
Wolf, J.A.: Fine structure of Hermitian symmetric spaces. In: Symmetric Spaces (Short Courses, Washington University, St. Louis, Mo. 1969–1970), Pure and Applied Mathematics, vol. 8, 271–357. Marcel Dekker, New York (1972)
Wolf, J.A.: Spaces of constant curvature, 5th edn. Publish or Perish, Wilmington, Delaware (1984)
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Geatti, L., Iannuzzi, A. & Loeb, JJ. A characterization of bounded symmetric domains of type IV. manuscripta math. 135, 183–202 (2011). https://doi.org/10.1007/s00229-011-0436-y
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DOI: https://doi.org/10.1007/s00229-011-0436-y