拟凸Hartogs域到复空间形式的全纯等距嵌入映射的存在性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (6): 1511-1524.

拟凸Hartogs域到复空间形式的全纯等距嵌入映射的存在性

郝毅红^1,*(),王安²()

¹ 西北大学数学学院西安 710127
² 首都师范大学数学科学学院北京 100048

收稿日期:2019-05-24 出版日期:2020-12-26 发布日期:2020-12-29
通讯作者: 郝毅红 E-mail:haoyihong@nwu.edu.cn;wangan@mail.cnu.edu.cn
作者简介:王安, E-mail:wangan@mail.cnu.edu.cn
基金资助:
国家自然科学基金(11601422);国家自然科学基金(11671270);国家自然科学基金(11871044);北京市自然科学基金(1182008);河北省自然科学基金(A2019106037);陕西省科技厅自然科学基础研究计划(2019JQ-398);陕西省教育厅专项科学研究计划(19JK0841);西北大学自然科学基金(15NW23)

Kähler Immersions of Pseudoconvex Hartogs Domains into Complex Space Forms

Yihong Hao^1,*(),An Wang²()

¹ Department of Mathematics, Northwest University, Xi'an 710127
² School of Mathematical Sciences, Capital Normal University, Beijing 100048

Received:2019-05-24 Online:2020-12-26 Published:2020-12-29
Contact: Yihong Hao E-mail:haoyihong@nwu.edu.cn;wangan@mail.cnu.edu.cn
Supported by:
the NSFC(11601422);the NSFC(11671270);the NSFC(11871044);the Beijing Municipal Natural Science Foundation(1182008);the NSF of Hebei Province(A2019106037);the NSF of Shannxi Province(2019JQ-398);the Scientific Research Program of Shaanxi Provincial Education Department(19JK0841);the Science Research Foundation of Northwest University(15NW23)

摘要/Abstract

摘要：

在 ${\Bbb C}^{n}$ 中的有界拟凸Hartogs域 $\Omega$ 上, 存在一个自然的Kähler度量 $g^{\Omega}$ .该文将研究有界拟凸Hartogs域 $(\Omega, h g^{\Omega})$ 到复空间形式的全纯等距嵌入映射的存在性问题.

关键词: 全纯等距嵌入映射, 复空间形式, 拟凸Hartogs域

Abstract:

Let $\Omega$ be a bounded pseudoconvex Hartogs domain in ${\Bbb C}^{n}$ . There exists a natural Kähler metric $g^{\Omega}$ in terms of its defining function. In this paper, we study the existence of Kähler immersions of $(\Omega, h g^{\Omega})$ into finite and infinite dimensional complex space forms for $h>0$ .

Key words: Kähler immersion, Complex space form, Pseudoconvex Hartogs domain

中图分类号:

O174.5

郝毅红,王安. 拟凸Hartogs域到复空间形式的全纯等距嵌入映射的存在性[J]. 数学物理学报, 2020, 40(6): 1511-1524.

Yihong Hao,An Wang. Kähler Immersions of Pseudoconvex Hartogs Domains into Complex Space Forms[J]. Acta mathematica scientia,Series A, 2020, 40(6): 1511-1524.

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