| 摘要: |
| 具有特定度量的某些域与不同复空间型的公共子流形问题一直是多复变的一个热门研究课题.基于Ma等人关于华罗庚域E(q1, q2,…,qm,Ω;1, p2,…，pm)与复欧氏空间不相关性的研究基础,本文突破其参数固定为1的限定条件,将其推广成圆型齐性域上的一类华罗庚域EΩ = E(q1,…,qm, Ω;p1,…,pm),并证明了具有 Bergman度量的域EΩ与具有平坦度量的复欧氏空间没有公共的Kähler子流形, 即二者是不相关的. |
| 关键词: 华罗庚域 全纯等距嵌入 Nash函数 复欧氏空间 |
| DOI： |
| 分类号:O174.56 |
| 基金项目:国家自然科学基金项目(12026420);吉林省科技发展计划项目(YDZJ202201ZYTS627);吉林省教育厅“十三五”科学技术项目(JJKH20200405KJ). |
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| COMMON SUBMANIFOLDS OF A CLASS OF HUA DOMAINS BASED ON CIRCULAR HOMOGENEITY DOMAINS AND COMPLEX EUCLIDEAN SPACES |
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CHENG Xiao-liang, ZHANG Hong-xu, FU Yu
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College of Mathematics and Computer, Jilin Normal University, Siping 136000, China
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| Abstract: |
| The problem of common submanifolds between certain domains with specific metrics and different complex spaces has long been a hot research topic in multi complex variables.Based on the research of Ma et al regarding the irrelevance of Hua domains E(q1, q2,…,qm,Ω;1, p2,…，pm) and complex Euclidean spaces, this paper overcomes the limitation of fixing the parameter at l and generalizes it to a class of Hua domains EΩ = E(q1,…,qm, Ω;p1,…,pm) on circular homogeneous domains. It is proven that there is no common Kähler submanifolds between domains EΩ with Bergman metric and complex Euclidean spaces with flat metric, indicating that the two are not related. |
| Key words: Hua domain holomorphic isometric embedding Nash function complex Euclidean spaces |
