ON MANNHEIM PARTNER CURVES IN THREE DIMENSIONAL LIE GROUPS

被引：11
|
作者：
Gok, Ismail [1 ]
Okuyucu, O. Zeki [2 ]
Ekmekci, Nejat [1 ]
Yayli, Yusuf [1 ]
机构：
[1] Ankara Univ, Fac Sci, Dept Math, TR-06100 Ankara, Turkey
[2] Bilecik Seyh Edebali Univ, Fac Sci & Arts, Dept Math, TR-11210 Bilecik, Turkey
来源：
MISKOLC MATHEMATICAL NOTES | 2014年 / 15卷 / 02期
关键词：
Mannheim curves; Lie groups; HARMONIC CURVATURES; HELICES; SPACE;
D O I：
10.18514/MMN.2014.682
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we define Mannheim partner curves in a three dimensional Lie group G with a bi-invariant metric. The main result of the paper is given as (Theorem 4): A curve ff W I R ! G with the Frenet apparatus fT; N; B; ; g is a Mannheim partner curve if and only if 1CH 2 D 1 where , are constants and H is the harmonic curvature function of the curve ff :
引用
收藏
页码：467 / 479
页数：13
相关论文
共 50 条
  • [1] BERTRAND CURVES IN THREE DIMENSIONAL LIE GROUPS
    Okuyucu, O. Zeki
    Gok, Ismail
    Yayli, Yusuf
    Ekmekci, Nejat
    MISKOLC MATHEMATICAL NOTES, 2017, 17 (02) : 999 - 1010
  • [2] SMARANDACHE CURVES IN THREE DIMENSIONAL LIE GROUPS
    Okuyucu, O. Zeki
    Degirmen, Caner
    Yildiz, O. Gokmen
    COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2019, 68 (01): : 1175 - 1185
  • [3] ON THE DARBOUX ROTATION AXIS OF CURVES IN THREE-DIMENSIONAL LIE GROUPS
    Ozturk, Ufuk
    Erdal, Gulay
    FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2023, 38 (03): : 649 - 658
  • [4] SPINOR REPRESENTATIONS OF FRAMED CURVES IN THE THREE-DIMENSIONAL LIE GROUPS
    Isbilir, Zehra
    Yazici, Bahar Dogan
    Tosun, Murat
    JOURNAL OF DYNAMICAL SYSTEMS AND GEOMETRIC THEORIES, 2023, 21 (01) : 61 - 83
  • [5] Framed curves in three-dimensional Lie groups and a Berry phase model
    Yazici, Bahar Dogan
    Okuyucu, Osman Zeki
    Tosun, Murat
    JOURNAL OF GEOMETRY AND PHYSICS, 2022, 182
  • [6] Bertrand and Mannheim Curves of Spherical Framed Curves in a Three-Dimensional Sphere
    Takahashi, Masatomo
    Yu, Haiou
    MATHEMATICS, 2022, 10 (08)
  • [7] On Mannheim partner curves in E3
    Orbay, Keziban
    Kasap, Emin
    INTERNATIONAL JOURNAL OF THE PHYSICAL SCIENCES, 2009, 4 (05): : 261 - 264
  • [8] ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE
    Ozkaldi, Siddika
    Ilarslan, Kazim
    Yayli, Yusuf
    HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2011, 40 (05): : 649 - 661
  • [9] Mannheim partner curves in 3-space
    Liu, Huili
    Wang, Fan
    JOURNAL OF GEOMETRY, 2008, 88 (1-2) : 120 - 126
  • [10] Isometry groups of three-dimensional Lie groups
    Cosgaya, Ana
    Reggiani, Silvio
    ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2022, 61 (04) : 831 - 845
12345