On the Proper Holomorphic Mappings between Equidimensional Hartogs Domains over Hermitian Symmetric Manifolds

被引：0

作者：

Bi, En Chao ^{[1
]}

机构：

[1] Qingdao Univ, Sch Math & Stat, Qingdao 266071, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2024年 / 40卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Proper holomorphic mapping; Hartogs domains; Hermitian symmetric manifolds; RIGIDITY; MAPS; SPACES;

D O I：

10.1007/s10114-023-2054-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a family of Hartogs domains fibred over Hermitian symmetric manifolds being a unit ball in DOUBLE-STRUCK CAPITAL Cm. The aim of the present study is to establish the rigidity results about proper holomorphic mappings between two equidimensional Hartogs domains over Hermitian symmetric manifolds. In particular, we can fully determine its biholomorphic equivalence and automorphism group.

引用

页码：1215 / 1228

页数：14

共 30 条

[1] AUTOMORPHISMS OF THE HARTOGS TYPE DOMAINS OVER CLASSICAL SYMMETRIC DOMAINS [J].

Ahn, Heungju ;

Byun, Jisoo ;

Park, Jong-Do .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2012, 23 (09)

[2] PROPER HOLOMORPHIC MAPPINGS IN CN [J].

ALEXANDER, H .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1977, 26 (01) :137-146

[3] PROPER SELF MAPS OF WEAKLY PSEUDO-CONVEX DOMAINS [J].

BEDFORD, E ;

BELL, S .

MATHEMATISCHE ANNALEN, 1982, 261 (01) :47-49

[4] PROPER HOLOMORPHIC MAPPINGS BETWEEN CIRCULAR DOMAINS [J].

BELL, SR .

COMMENTARII MATHEMATICI HELVETICI, 1982, 57 (04) :532-538

[5] On the rigidity of proper holomorphic mappings for the Bergman-Hartogs domains [J].

Bi, Enchao .

BULLETIN DES SCIENCES MATHEMATIQUES, 2022, 175

[6] The Kobayashi Pseudometric for the Fock-Bargmann-Hartogs Domain and Its Application [J].

Bi, Enchao ;

Su, Guicong ;

Tu, Zhenhan .

JOURNAL OF GEOMETRIC ANALYSIS, 2020, 30 (01) :86-106

[7] RIGIDITY OF PROPER HOLOMORPHIC MAPPINGS BETWEEN GENERALIZED FOCK-BARGMANN-HARTOGS DOMAINS [J].

Bi, Enchao ;

Tu, Zhenhan .

PACIFIC JOURNAL OF MATHEMATICS, 2018, 297 (02) :277-297

[8]

CHIRKA EM, 1989, COMPLEX ANAL SETS

[9] FUNCTION-SPACES AND REPRODUCING KERNELS ON BOUNDED SYMMETRIC DOMAINS [J].

FARAUT, J ;

KORANYI, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 1990, 88 (01) :64-89

[10] On canonical metrics on Cartan-Hartogs domains [J].

Feng, Zhiming ;

Tu, Zhenhan .

MATHEMATISCHE ZEITSCHRIFT, 2014, 278 (1-2) :301-320

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