scholarly journals A Note on the Bergman metric of Bounded homogeneous Domains

2007 ◽  
Vol 186 ◽  
pp. 157-163 ◽  
Author(s):  
Chifune Kai ◽  
Takeo Ohsawa
Keyword(s):  
Potential Function ◽  
Bergman Metric ◽  
Homogeneous Domain ◽  
Homogeneous Domains ◽  
Bounded Homogeneous Domain

AbstractWe show that the Bergman metric of a bounded homogeneous domain has a potential function whose gradient has a constant norm with respect to the Bergman metric, and further that this constant is independent of the choice of such a potential function.

Some Properties of Bounded Holomorphic Mappings Defined on Bounded Homogeneous Domains

1986 ◽  
Vol 29 (3) ◽  
pp. 358-364
Author(s):  
Yoshihisa Kubota
Keyword(s):  
Holomorphic Mapping ◽  
Holomorphic Mappings ◽  
Homogeneous Domain ◽  
Homogeneous Domains ◽  
Bounded Holomorphic ◽  
Bounded Homogeneous Domain

AbstractLet F be a bounded holomorphic mapping defined on a bounded homogeneous domain in ℂN. We study the relation between the Jacobian JF(z) and the radius dF(z) of uni valence of F.

Generalization of Schwarz-Pick Lemma to Invariant Volume

1969 ◽  
Vol 21 ◽  
pp. 669-674
Author(s):  
K. T. Hahn ◽  
Josephine Mitchell
Keyword(s):  
Euclidean Space ◽  
Explicit Form ◽  
Bounded Domain ◽  
Kähler Manifold ◽  
Siegel Domain ◽  
Homogeneous Domain ◽  
Kahler Manifold ◽  
Invariant Volume ◽  
Complex Euclidean Space ◽  
Bounded Homogeneous Domain

In this paper we give an extension of (6, Theorem 1), using a similar method of proof, to every homogeneous Siegel domain of second kind which can be mapped biholomorphically into a Kâhler manifold of a certain class (Theorem 1). Then by a well-known result of Vinberg, Gindikin, and Pjateckiï-Sapiro (10) that every bounded homogeneous domain D,contained in a complex euclidean space CN,can be mapped biholomorphically onto an affinely homogeneous Siegel domain of second kind, the theorem follows for D(Theorem 2). (6, Theorem 1) is a generalization of the Ahlfors version of the Schwarz-Pick lemma in C1(1) to invariant volume for a star-like homogeneous bounded domain in CN;see also (4). In § 3 we give the inequality for a special non-symmetric Siegel domain of second kind using an explicit form of TD(z, )due to Lu (7).

Bergman–Hartogs domains and their automorphisms

2019 ◽  
pp. 316-323
Author(s):  
Guy ROOS
Keyword(s):  
Automorphism Groups ◽  
Symmetric Domain ◽  
Bounded Symmetric Domain ◽  
Homogeneous Domain ◽  
Hartogs Domains ◽  
Bounded Homogeneous Domain

For Cartan–Hartogs domains and also for Bergman–Hartogs domains, the determination of their automorphism groups is given for the cases when the base is any bounded symmetric domain and a general bounded homogeneous domain respectively.

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