Rational Curves in the Three-dimensional Sphere

被引：4
|
作者：
Georgiev, Georgi H. [1 ]
机构：
[1] Konstantin Preslavsky Univ Shumen, Fac Math & Informat, Shumen, Bulgaria
来源：
APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS | 2010年 / 1293卷
关键词：
Three-dimensional sphere; Bezier curves; Quaternion algebra;
D O I：
10.1063/1.3515576
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the three-dimensional sphere as a hypersurface embedded in the four-dimensional Euclidean space. The pre-images of polynomial and rational curves in the Euclidean 3-space under stereographic projection form a special class of rational curves on 3-sphere. We investigate these spherical curves in terms of Cartesian coordinates and quaternions.
引用
收藏
页码：133 / 140
页数：8
相关论文
共 50 条
  • [1] Rectifying curves in the three-dimensional sphere
    Lucas, Pascual
    Antonio Ortega-Yaguees, Jose
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 421 (02) : 1855 - 1868
  • [2] Bertrand curves in the three-dimensional sphere
    Lucas, Pascual
    Antonio Ortega-Yaguees, Jose
    [J]. JOURNAL OF GEOMETRY AND PHYSICS, 2012, 62 (09) : 1903 - 1914
  • [3] Bertrand and Mannheim Curves of Spherical Framed Curves in a Three-Dimensional Sphere
    Takahashi, Masatomo
    Yu, Haiou
    [J]. MATHEMATICS, 2022, 10 (08)
  • [4] Global Differential Geometry of Curves in Three-Dimensional Heisenberg Group and CR Sphere
    Hung-Lin Chiu
    Pak Tung Ho
    [J]. The Journal of Geometric Analysis, 2019, 29 : 3438 - 3469
  • [5] Global Differential Geometry of Curves in Three-Dimensional Heisenberg Group and CR Sphere
    Chiu, Hung-Lin
    Ho, Pak Tung
    [J]. JOURNAL OF GEOMETRIC ANALYSIS, 2019, 29 (04) : 3438 - 3469
  • [6] On Characterizing a Three-Dimensional Sphere
    Bin Turki, Nasser
    Deshmukh, Sharief
    Vilcu, Gabriel-Eduard
    [J]. MATHEMATICS, 2021, 9 (24)
  • [7] A study of three-dimensional curves
    Mardia, KV
    Baczkowski, AJ
    Feng, X
    Millner, PA
    [J]. JOURNAL OF APPLIED STATISTICS, 1996, 23 (01) : 139 - 148
  • [8] Three-dimensional dynamo waves in a sphere
    Gubbins, D
    Gibbons, S
    [J]. GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS, 2002, 96 (06): : 481 - 498
  • [9] SLANT HELICES IN THE THREE-DIMENSIONAL SPHERE
    Lucas, Pascual
    Ortega-Yagues, Jose Antonio
    [J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2017, 54 (04) : 1331 - 1343
  • [10] Generation of modes on the three-dimensional sphere
    Burlankov, D. E.
    [J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2007, 150 (03) : 355 - 376
12345