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
收藏
页码：189 / 199
页数：11
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