NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES

doi:10.1007/s10473-021-0606-2

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (6): 1887-1895.doi: 10.1007/s10473-021-0606-2

NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES

孙道椿¹, 霍颖莹², 柴富杰³

1. School of Mathematics, South China Normal University, Guangzhou 510631, China;
2. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China;
3. School of Financial Mathematics&Statistics, Guangdong University of Finance, Guangzhou 510521, China

收稿日期:2021-03-11 修回日期:2021-07-11 出版日期:2021-12-25 发布日期:2021-12-27
通讯作者: Fujie CHAI,E-mail:chaifujie@sina.com E-mail:chaifujie@sina.com
作者简介:Daochun SUN,E-mail:1457330943@qq.com;Yingying HUO,E-mail:huoyingy@gdut.edu.cn
基金资助:
The second author was supported by the National Natural Science Foundation of China (11501127), Foundation for Distinguished Young Talents in Higher Education of Guangdong Province (2014KQNCX068). The third author was supported by the Foundation of Guangzhou Civil Aviation College (18X0428).

NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES

Daochun SUN¹, Yingying HUO², Fujie CHAI³

1. School of Mathematics, South China Normal University, Guangzhou 510631, China;
2. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China;
3. School of Financial Mathematics&Statistics, Guangdong University of Finance, Guangzhou 510521, China

Received:2021-03-11 Revised:2021-07-11 Online:2021-12-25 Published:2021-12-27
Supported by:
The second author was supported by the National Natural Science Foundation of China (11501127), Foundation for Distinguished Young Talents in Higher Education of Guangdong Province (2014KQNCX068). The third author was supported by the Foundation of Guangzhou Civil Aviation College (18X0428).

摘要/Abstract

摘要： In this paper, we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces. Then, we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces. These results generalize the Montel-type normal criterion of holomorphic curves.

关键词: complex projective spaces, holomorphic curves, holomorphic mappings, normal families, restricted hyperplanes

Abstract: In this paper, we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces. Then, we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces. These results generalize the Montel-type normal criterion of holomorphic curves.

Key words: complex projective spaces, holomorphic curves, holomorphic mappings, normal families, restricted hyperplanes

中图分类号:

30D45

孙道椿, 霍颖莹, 柴富杰. NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES[J]. 数学物理学报(英文版), 2021, 41(6): 1887-1895.

Daochun SUN, Yingying HUO, Fujie CHAI. NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES[J]. Acta mathematica scientia,Series B, 2021, 41(6): 1887-1895.

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NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES

NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES

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