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
相关论文
共 44 条
  • [1] NON-DEVELOPABLE RULED SURFACES WITH TIMELIKE RULING IN MINKOWSKI 3-SPACE
    Yang, Yun
    Yu, Yanhua
    BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2015, 52 (04) : 1339 - 1351
  • [2] Non-developable ruled surfaces in Euclidean 3-spaces
    Yoon, Dae Won
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2007, 38 (04) : 281 - 290
  • [3] Structure and characterization of ruled surfaces in Euclidean 3-space
    Yu, Yanhua
    Liu, Huili
    Dal Jung, Seoung
    APPLIED MATHEMATICS AND COMPUTATION, 2014, 233 : 252 - 259
  • [4] Quasi Ruled Surfaces in Euclidean 3-space
    Elsharkawy, Ayman
    Elsayied, Hoda K.
    Refaat, Aya
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2025, 18 (01):
  • [5] On non-developable ruled surfaces in Lorentz-Minkowski 3-spaces
    Kim, Young Ho
    Yoon, Dae Won
    TAIWANESE JOURNAL OF MATHEMATICS, 2007, 11 (01): : 197 - 214
  • [6] ON THE SECOND GAUSSIAN CURVATURE OF RULED SURFACES IN EUCLIDEAN 3-SPACE
    Yoon, Dae Won
    TAMKANG JOURNAL OF MATHEMATICS, 2006, 37 (03): : 221 - 226
  • [7] A STUDY ON RULED SURFACE IN EUCLIDEAN 3-SPACE
    Tuncer, Yilmaz
    Ekmekci, Nejat
    JOURNAL OF DYNAMICAL SYSTEMS AND GEOMETRIC THEORIES, 2010, 8 (01) : 49 - 57
  • [8] Prediction of cutting forces in flank milling of parts with non-developable ruled surfaces
    Liping WANG
    Hao SI
    Liheng GU
    Chinese Journal of Aeronautics , 2019, (07) : 1788 - 1796
  • [9] Prediction of cutting forces in flank milling of parts with non-developable ruled surfaces
    Wang, Liping
    Si, Hao
    Gu, Liheng
    CHINESE JOURNAL OF AERONAUTICS, 2019, 32 (07) : 1788 - 1796
  • [10] RULED SURFACES GENERATED BY SALKOWSKI CURVE AND ITS FRENET VECTORS IN EUCLIDEAN 3-SPACE
    Cakil, Ebru
    Mazlum, Sumeyye gur
    KOREAN JOURNAL OF MATHEMATICS, 2024, 32 (02): : 259 - 284
12345