数学物理学报 ›› 2023, Vol. 43 ›› Issue (3): 657-668.

• •    下一篇

迷向增长曲面的结构表达式

钱金花1,*(),卞金鑫1,付雪山2   

  1. 1东北大学理学院 沈阳 110819
    2沈阳工业大学理学院 沈阳 110870
  • 收稿日期:2022-05-12 修回日期:2023-02-06 出版日期:2023-06-26 发布日期:2023-06-01
  • 通讯作者: 钱金花 E-mail:qianjinhua@mail.neu.edu.cn
  • 基金资助:
    国家自然科学基金(11801065);沈阳工业大学青年教师科研能力培育基金(QNPY202209-24)

Structure Expression Form of Isotropic Growth Surface

Qian Jinhua1,*(),Bian Jinxin1,Fu Xueshan2   

  1. 1College of Science, Northeastern University, Shenyang 110819
    2College of Science, Shenyang University of Technology, Shenyang 110870
  • Received:2022-05-12 Revised:2023-02-06 Online:2023-06-26 Published:2023-06-01
  • Contact: Jinhua Qian E-mail:qianjinhua@mail.neu.edu.cn
  • Supported by:
    NSFC(11801065);Research Ability Cultivation Fund for Young Teachers of Shenyang University of Technology(QNPY202209-24)

摘要:

在三维复空间中研究由迷向曲线按照给定的生长速度生成的迷向增长曲面. 利用迷向生成曲线的结构函数探索迷向增长曲面的结构表达式. 作为一项重要的应用, 讨论由特殊的迷向曲线即迷向螺线生成的迷向增长曲面的结构表达式, 同时给出一些具体实例表明此类增长曲面的生成过程.

关键词: 复空间, 迷向曲线, 增长曲面, 迷向螺线, 结构函数

Abstract:

The isotropic growth surface in complex 3-space is investigated by evolving an isotropic curve as dictated growth velocity. The structure expression form of the isotropic growth surface is explored by the aid of the structure function of its generating isotropic curve. As an important application, the isotropic growth surface initiated by the isotropic helix is discussed deeply and explicitly. At the same time, several typical examples are constructed to characterize the generating process of such growth surfaces.

Key words: Complex space, Isotropic curve, Growth surface, Isotropic helix, Structure function

中图分类号: 

  • O186