A new approach to Bertrand curves in Euclidean 3-space

被引：12
|
作者：
Camci, Cetin [1 ]
Ucum, Ali [2 ]
Ilarslan, Kazim [2 ]
机构：
[1] Onsekiz Mart Univ, Dept Math, Fac Sci & Arts, Canakkale, Turkey
[2] Kirikkale Univ, Dept Math, Fac Sci & Arts, Kirikkale, Turkey
来源：
JOURNAL OF GEOMETRY | 2020年 / 111卷 / 03期
关键词：
Bertrand curves; General helices; Anti-Salkowski curves; Euclidean; 3-space;
D O I：
10.1007/s00022-020-00560-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, a new approach is given for Bertrand curves in 3-dimensional Euclidean space. According to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Bertrand curve in E-3. In addition, the related examples and graphs are given by showing that general helices and anti-Salkowski curves can be Bertrand curves or their mates, which is their new characterization.
引用
收藏
页数：15
相关论文
共 50 条
  • [1] A new approach to Bertrand curves in Euclidean 3-space
    Çetin Camci
    Ali Uçum
    Kazım İlarslan
    [J]. Journal of Geometry, 2020, 111
  • [2] Spherical Indicatrix of a New Approach to Bertrand Curves in Euclidean 3-space
    Tamta, Stuti
    Gupta, Ram Shankar
    [J]. KYUNGPOOK MATHEMATICAL JOURNAL, 2023, 63 (02): : 263 - 285
  • [3] On helices and Bertrand curves in Euclidean 3-space
    Babaarslan, Murat
    Yayli, Yusuf
    [J]. Mathematical and Computational Applications, 2013, 18 (01) : 1 - 11
  • [4] ON GENERALIZED BERTRAND CURVES IN EUCLIDEAN 3-SPACE
    Demir, Demet
    Ilarslan, Kazim
    [J]. FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2023, 38 (01): : 199 - 208
  • [5] New representations of Bertrand pairs in Euclidean 3-space
    Tuncer, Yilmaz
    Unal, Serpil
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (04) : 1833 - 1842
  • [6] Surfaces Family with Bertrand Curves as Common Asymptotic Curves in Euclidean 3-Space E3
    Aldossary, Maryam T.
    Abdel-Baky, Rashad A.
    [J]. SYMMETRY-BASEL, 2023, 15 (07):
  • [7] On rectifying curves in Euclidean 3-space
    Deshmukh, Sharief
    Chen, Bang-Yen
    Alshammari, Sana Hamoud
    [J]. TURKISH JOURNAL OF MATHEMATICS, 2018, 42 (02) : 609 - 620
  • [8] ON TIMELIKE BERTRAND CURVES IN MINKOWSKI 3-SPACE
    Ucum, Ali
    Ilarslan, Kazim
    [J]. HONAM MATHEMATICAL JOURNAL, 2016, 38 (03): : 467 - 477
  • [9] Generalized Bertrand Curves in Minkowski 3-Space
    Zhang, Chunxiao
    Pei, Donghe
    [J]. MATHEMATICS, 2020, 8 (12) : 1 - 11
  • [10] Some new types of associated curves in Euclidean 3-space
    Ozdogan, Sibel
    Tuncer, O. Ogulcan
    Gok, Ismail
    Yayli, Yusuf
    [J]. ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2018, 26 (01): : 205 - 221
12345