Invariants of non-developable ruled surfaces in Euclidean 3-space

被引：12

作者：

Liu, Huili ^{[1
]}

Yu, Yanhua ^{[1
]}

Dal Jung, Seoung ^{[2
]}

机构：

[1] Northeastern Univ, Dept Math, Shenyang 110004, Liaoning, Peoples R China

[2] Jeju Natl Univ, Dept Math, Jeju 690756, South Korea

来源：

BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY | 2014年 / 55卷 / 01期

关键词：

Spherical curve; Frenet formula; Ruled surface; Structure function; Pitch function; Angle function of pitch; Center of torsion;

D O I：

10.1007/s13366-013-0177-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, using the classical methods of differential geometry, we define invariants of non-developable ruled surfaces in Euclidean 3-space, called structure functions, and show kinematics meaning of these invariants. We also generalize the notion of the angle of pitch of a closed ruled surface to any non-developable ruled surface. Then we discuss the properties of these invariants and give a kind of classification of the non-developable ruled surfaces in Euclidean 3-space with the theories of these invariants.

引用

页码：189 / 199

页数：11

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