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M3 (δ0)⊂E2 4 9 3-Uzayında non-Dejenere Eğriler Tarafından Elde Edilen Helis ve Slant Helisler

Year 2021, Volume: 16 Issue: 1, 113 - 117, 15.03.2021

Abstract

References

  • [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

Year 2021, Volume: 16 Issue: 1, 113 - 117, 15.03.2021

Abstract

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.

References

  • [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.
There are 19 citations in total.

Details

Primary Language English
Journal Section TJST
Authors

Fatma Almaz 0000-0002-1060-7813

Mihriban Külahci 0000-0002-8621-5779

Publication Date March 15, 2021
Submission Date January 29, 2021
Published in Issue Year 2021 Volume: 16 Issue: 1

Cite

APA Almaz, F., & Külahci, M. (2021). The Helix and Slant Helices Generated by non-Degenerate Curves in M3(δ0)⊂E24. Turkish Journal of Science and Technology, 16(1), 113-117.
AMA Almaz F, Külahci M. The Helix and Slant Helices Generated by non-Degenerate Curves in M3(δ0)⊂E24. TJST. March 2021;16(1):113-117.
Chicago Almaz, Fatma, and Mihriban Külahci. “The Helix and Slant Helices Generated by Non-Degenerate Curves in M3(δ0)⊂E24”. Turkish Journal of Science and Technology 16, no. 1 (March 2021): 113-17.
EndNote Almaz F, Külahci M (March 1, 2021) The Helix and Slant Helices Generated by non-Degenerate Curves in M3(δ0)⊂E24. Turkish Journal of Science and Technology 16 1 113–117.
IEEE F. Almaz and M. Külahci, “The Helix and Slant Helices Generated by non-Degenerate Curves in M3(δ0)⊂E24”, TJST, vol. 16, no. 1, pp. 113–117, 2021.
ISNAD Almaz, Fatma - Külahci, Mihriban. “The Helix and Slant Helices Generated by Non-Degenerate Curves in M3(δ0)⊂E24”. Turkish Journal of Science and Technology 16/1 (March 2021), 113-117.
JAMA Almaz F, Külahci M. The Helix and Slant Helices Generated by non-Degenerate Curves in M3(δ0)⊂E24. TJST. 2021;16:113–117.
MLA Almaz, Fatma and Mihriban Külahci. “The Helix and Slant Helices Generated by Non-Degenerate Curves in M3(δ0)⊂E24”. Turkish Journal of Science and Technology, vol. 16, no. 1, 2021, pp. 113-7.
Vancouver Almaz F, Külahci M. The Helix and Slant Helices Generated by non-Degenerate Curves in M3(δ0)⊂E24. TJST. 2021;16(1):113-7.