关于圆柱螺线主法线曲面一些性质的研究

楚雄师范学院学报 ›› 2024, Vol. 39 ›› Issue (3): 60-66.

关于圆柱螺线主法线曲面一些性质的研究

王雪梅¹, 梁林^2,*

1.楚雄师范学院教育学院,云南楚雄 675000;
2.楚雄师范学院数学与计算机科学学院,云南楚雄 675000

收稿日期:2023-08-22 出版日期:2024-05-20 发布日期:2024-06-05
通讯作者: *梁林（1967–）,男,教授,研究方向为微分几何。 E-mail： 1749037312@qq.com,Tel. 13987872618
作者简介:王雪梅（1994–）,女,助教,研究方向为非线性偏微分方程。E-mail： 1749037312@qq.com,Tel. 18487383731

A Study on Some Properties of the Main Normal Surface of a Cylindrical Spiral

WANG Xuemei¹, LIANG Lin²

1. School of Education, Chuxiong Normal University, Chuxiong, Yunnan Province 675000;
2. School of Mathematics and Computer Science, Chuxiong Normal University, Chuxiong, Yunnan Province 675000

Received:2023-08-22 Online:2024-05-20 Published:2024-06-05

摘要/Abstract

摘要： 曲面的性质一直是微分几何研究的一个热点问题,而圆柱螺线又是几何学的最重要曲线。本文以圆柱螺线为对象,运用微分几何方法,对圆柱螺线的主法线曲面的有关几何性质进行了研究,获得了圆柱螺线的主法线曲面的渐近曲线、曲率线、法曲率、主曲率、高斯曲率、平均曲率等结论,为深入研究圆柱螺线的主法线曲面子流形奠定基础。

关键词: 圆柱螺线, 主法线曲面, 平均曲率, 高斯曲率, 主曲率

Abstract: The properties of surfaces have always been a hot issue in the study of differential geometry, and cylindrical solenoid is the most important curve in the geometry. In this paper, differential geometry methods are used to investigate the geometric properties related to the principal normal surfaces of cylindrical solenoids, with the cylindrical solenoid as the object. The study has obtained conclusions on the asymptotic curves, lines of curvature, normal curvature, principal curvature, Gaussian curvature and mean curvature of the principal normal surfaces of cylindrical solenoids. The results of the study provide a basis for deepening study on the main normal surface subfluidization of cylindrical solenoid.

Key words: cylindrical spiral, principal normal surface, average curvature, Gaussian curvature, principal curvature

中图分类号:

O186.1

王雪梅, 梁林. 关于圆柱螺线主法线曲面一些性质的研究[J]. 楚雄师范学院学报, 2024, 39(3): 60-66.

WANG Xuemei, LIANG Lin. A Study on Some Properties of the Main Normal Surface of a Cylindrical Spiral[J]. Journal of Chuxiong Normal University, 2024, 39(3): 60-66.