M3 (δ0)⊂E2 4 9 3-Uzayında non-Dejenere Eğriler Tarafından Elde Edilen Helis ve Slant Helisler
Yıl 2021,
Cilt: 16 Sayı: 1, 113 - 117, 15.03.2021
Fatma Almaz
,
Mihriban Külahci
Kaynakça
- [1] Ali AT, Lopez R. Timelike B2-Slant Helices in Minkowski Space E14. Archıvum Mathematicum(BRNO) Tomus, 2010; 46: 39-46.
- [2] Ali AT. Position vectors of spacelike general helices in Minkowski 3-Space. Nonlinear Analysis 2010; 73: 1118-1126.
- [3] Ali AT, Lopez R, Turgut M. k-type partially null and pseudo null slant helices in Minkowski 4-Space. Math. Commun. 2012; 17: 93-103.
- [4] Ali AT, Turgut M. Some Characterizations of slant helices in the Euclidean En. arXiv: 0904.1187v1 2009; 8pp.
- [5] Barros M, Ferrandes A, Lukas P, Mero.no MA. General helices in the three dimensional Lorentzian space forms. Rocky Mountain J. Math 2001; 31(2): 373-388.
- [6] Camci C, Ilarslan K, Kula L, Hacisalihoglu HH. Harmonic curvatures and generalized helices in En. Chaos, Solitons and Fractals 2009; 40: 2590-2596.
- [7] Ferrandez A, Gimenez A, Lucas P. Null generalized helices in Lorentz-Minkowski Spaces. Journal of Physics A: Math. and General 2002; 35(39): 8243-8251.
- [8] Gluck H. Higher curvature of curves in Euclidean space. Amer. Math. Monthly 1996; 73: 699-704.
- [9] Izumiya S, Takeuchi N. New special curves and devalopable surface. Turk J. Math. 2004; 28: 153-163.
- [10] Ilarslan K, Boyacioglu O. Position vectors of a timelike and a null helix in Minkowski 3-Space. Chaos Solitons and Fractals 2008; 38: 1383-1389.
- [11] Kula L, Yayli Y, On slant helix and its spherical indicatrix. App. Math. and Computation 2005; 169: 600-607.
- [12] Kulahci M, Bektaş M, Ergüt M. Curves of AW(k)-type in 3-dimensional null cone. Physics Letters A371 2007; 275-277.
- [13] Kulahci M, Almaz F. Some characterizations of osculating curves in the lightlike cone. Bol. Soc. Paran. Math. 2017; 35(2): 39-48, 2017.
- [14] Kulahci MA, Almaz F, Bektaş M. On helices and slant helices in the lightlike cone. Honam Mathematical J. 2018; 40(2): 305-314.
- [15] Liu H. Curves in the lightlike cone. Contributions to Algebra and Geometry Volume 2004; 45(1): 291-303.
- [16] Millman RS, Parker GD. Elements of differential geometry, Prentice-Hall Inc. Englewood Cliffs, N. J., 1977.
- [17] Onder M, Kocayigit H. Kazaz M. Spacelike helices in Minkowski 4-Space E14 Ann Univ. Ferrara 2010; 56: 335-343.
- [18] O’Neill B. Semi-Riemannian Geometry, Academic Press, New York, 1983.
- [19] Turgut M, Yilmaz S. Some Characterizations of type-3 slant helices in Minkowski Space-time. Involve 2009; 2(1): 115-121.
The Helix and Slant Helices Generated by non-Degenerate Curves in M3(δ0)⊂E24
Yıl 2021,
Cilt: 16 Sayı: 1, 113 - 117, 15.03.2021
Fatma Almaz
,
Mihriban Külahci
Öz
In this paper, we investigate helix and slant helices using non-degenerate curves in term of Sabban frame in de Sitter 3-space or Anti de Sitter 3-space M3(δ0). Furthermore, in M3(δ0) 3-space the necessary and sufficient conditions for the non-degenerate curves to be slant helix are given.
Kaynakça
- [1] Ali AT, Lopez R. Timelike B2-Slant Helices in Minkowski Space E14. Archıvum Mathematicum(BRNO) Tomus, 2010; 46: 39-46.
- [2] Ali AT. Position vectors of spacelike general helices in Minkowski 3-Space. Nonlinear Analysis 2010; 73: 1118-1126.
- [3] Ali AT, Lopez R, Turgut M. k-type partially null and pseudo null slant helices in Minkowski 4-Space. Math. Commun. 2012; 17: 93-103.
- [4] Ali AT, Turgut M. Some Characterizations of slant helices in the Euclidean En. arXiv: 0904.1187v1 2009; 8pp.
- [5] Barros M, Ferrandes A, Lukas P, Mero.no MA. General helices in the three dimensional Lorentzian space forms. Rocky Mountain J. Math 2001; 31(2): 373-388.
- [6] Camci C, Ilarslan K, Kula L, Hacisalihoglu HH. Harmonic curvatures and generalized helices in En. Chaos, Solitons and Fractals 2009; 40: 2590-2596.
- [7] Ferrandez A, Gimenez A, Lucas P. Null generalized helices in Lorentz-Minkowski Spaces. Journal of Physics A: Math. and General 2002; 35(39): 8243-8251.
- [8] Gluck H. Higher curvature of curves in Euclidean space. Amer. Math. Monthly 1996; 73: 699-704.
- [9] Izumiya S, Takeuchi N. New special curves and devalopable surface. Turk J. Math. 2004; 28: 153-163.
- [10] Ilarslan K, Boyacioglu O. Position vectors of a timelike and a null helix in Minkowski 3-Space. Chaos Solitons and Fractals 2008; 38: 1383-1389.
- [11] Kula L, Yayli Y, On slant helix and its spherical indicatrix. App. Math. and Computation 2005; 169: 600-607.
- [12] Kulahci M, Bektaş M, Ergüt M. Curves of AW(k)-type in 3-dimensional null cone. Physics Letters A371 2007; 275-277.
- [13] Kulahci M, Almaz F. Some characterizations of osculating curves in the lightlike cone. Bol. Soc. Paran. Math. 2017; 35(2): 39-48, 2017.
- [14] Kulahci MA, Almaz F, Bektaş M. On helices and slant helices in the lightlike cone. Honam Mathematical J. 2018; 40(2): 305-314.
- [15] Liu H. Curves in the lightlike cone. Contributions to Algebra and Geometry Volume 2004; 45(1): 291-303.
- [16] Millman RS, Parker GD. Elements of differential geometry, Prentice-Hall Inc. Englewood Cliffs, N. J., 1977.
- [17] Onder M, Kocayigit H. Kazaz M. Spacelike helices in Minkowski 4-Space E14 Ann Univ. Ferrara 2010; 56: 335-343.
- [18] O’Neill B. Semi-Riemannian Geometry, Academic Press, New York, 1983.
- [19] Turgut M, Yilmaz S. Some Characterizations of type-3 slant helices in Minkowski Space-time. Involve 2009; 2(1): 115-121.