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ℚ𝟐 𝟑 ⊂ 𝐄𝟐 𝟒 Lightlike Koni 3-Uzayında Null Eğrilerin Elastik Olmayan Akış(İnextensible Flow) Eğrileri

Year 2021, Volume: 33 Issue: 2, 667 - 673, 15.09.2021
https://doi.org/10.35234/fumbd.871674

Abstract

Bir eğri veya yüzey akışı; eğer yay uzunluğu ve eğrilik korunursa uzatılamaz olarak adlandırılır. Fiziksel anlamda, elastik olmayan eğri(inextensible flows) ve yüzey akışları herhangi bir gerilme enerjisinin yokluğu ile karakterize edilir. Bu çalışmada 2 ideksli 4 boyutlu ℚ23 ⊂ E24 lightlike koni uzayında doğal Frenet çatısı kullanılarak ifade edilen bir null x: I → ℚ23 ⊂ E24 eğrisinin elastik olmayan akışı(inextensible flows) ifade edilerek matematiksel açıdan bazı karekterizasyonları verilmiştir.

References

  • [1] Abazari N, Bohner M, Sager I, Sedaghatdoost A. Spacelike curves in the lightlike cone. Appl. Math. Inf. Sci. 2018; 12(6): 1227–1236.
  • [2] Almaz F, Külahcı MA. A survey on magnetic curves in 2-dimensional lightlike cone. Malaya Journal of Matematik 2019; 7(3): 477-485.
  • [3] Almaz F, Külahcı MA. On x-magnetic Surfaces Generated by Trajectory of x-magnetic Curves in Null Cone. General Letters in Mathematics 2018; 5(2), pp.84-92.
  • [4] Bejancu A. Lightlike curves in Lorentz manifolds. Publ. Math. (Debr.) 1994; 44(1–2): 145–155.
  • [5] Bonnor WB, Null curves in a Minkowski space-time. Tensor 1969: 20: 229- 242.
  • [6] Chirikjian G, Burdick J. A modal approach to hyper-redundant manipulator kinematics IEEE Trans. Robot. Autom. 1994; 10: 343–354.
  • [7] Desbrun M, Cani-Gascuel MP. Active implicit surface for animation,.in: Proc. Graphics Interface—Canadian Inf. Process. Soc. 1998; 143–150.
  • [8] Duggal KL, Jin DH. Null Curves and Hypersurfaces of Semi-Riemannian Manifolds. London: World Scientific 2007.
  • [9] Gökmen O, Tosun M, Özkaldı Karakuş S, A note on inextensible flows of curves in En. Int. Electron. J. Geom. Vol. 2013; 6(2): 118–124.
  • [10] Körpinar T, Turhan E. A new version of inextensible flows of spacelike curves with timelike B2 in Minkowski space-time E41 . Differ. Equ. Dyn. Syst. Vol. 2013; 21(3): 281-290.
  • [11] Kulahci M. Investigation of a curve using Frenet frame in the lightlike cone. Open Phys. 2017; 15(1): 175–181.
  • [12] Kulahci,M, Almaz F, Bektaş M. On Helices And Slant Helices in The Lightlike Cone, Honam Mathematical J. 2018; 40(2): pp. 305–314.
  • [13] Kühnel W. Differential Geometry: Curves—Surfaces—Manifolds. Student Mathematical Library, vol. 77. Am. Math. Soc., Providence 2015.
  • [14] Liu H. Curves in the lightlike cone. Beitr. Algebra Geom. 2004; 45(1): 291–303.
  • [15] Liu H. Meng Q. Representation formulas of curves in a two-and three-dimensional lightlike cone. Results Math. 2011; 59(3–4): 437–451.
  • [16] O’Neill B. Semi-Riemannian geometry with applications to relativity. New York: Academic Press 1983.
  • [17] Sun J, Pei D. Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres. J. Nonlinear Sci. Appl. 2015; 8(3): 275–284.
  • [18] Unger DJ. Developable surfaces in elastoplastic fracture mechanics. Int. J. Fract. 1991; 50: 33–38.
Year 2021, Volume: 33 Issue: 2, 667 - 673, 15.09.2021
https://doi.org/10.35234/fumbd.871674

Abstract

References

  • [1] Abazari N, Bohner M, Sager I, Sedaghatdoost A. Spacelike curves in the lightlike cone. Appl. Math. Inf. Sci. 2018; 12(6): 1227–1236.
  • [2] Almaz F, Külahcı MA. A survey on magnetic curves in 2-dimensional lightlike cone. Malaya Journal of Matematik 2019; 7(3): 477-485.
  • [3] Almaz F, Külahcı MA. On x-magnetic Surfaces Generated by Trajectory of x-magnetic Curves in Null Cone. General Letters in Mathematics 2018; 5(2), pp.84-92.
  • [4] Bejancu A. Lightlike curves in Lorentz manifolds. Publ. Math. (Debr.) 1994; 44(1–2): 145–155.
  • [5] Bonnor WB, Null curves in a Minkowski space-time. Tensor 1969: 20: 229- 242.
  • [6] Chirikjian G, Burdick J. A modal approach to hyper-redundant manipulator kinematics IEEE Trans. Robot. Autom. 1994; 10: 343–354.
  • [7] Desbrun M, Cani-Gascuel MP. Active implicit surface for animation,.in: Proc. Graphics Interface—Canadian Inf. Process. Soc. 1998; 143–150.
  • [8] Duggal KL, Jin DH. Null Curves and Hypersurfaces of Semi-Riemannian Manifolds. London: World Scientific 2007.
  • [9] Gökmen O, Tosun M, Özkaldı Karakuş S, A note on inextensible flows of curves in En. Int. Electron. J. Geom. Vol. 2013; 6(2): 118–124.
  • [10] Körpinar T, Turhan E. A new version of inextensible flows of spacelike curves with timelike B2 in Minkowski space-time E41 . Differ. Equ. Dyn. Syst. Vol. 2013; 21(3): 281-290.
  • [11] Kulahci M. Investigation of a curve using Frenet frame in the lightlike cone. Open Phys. 2017; 15(1): 175–181.
  • [12] Kulahci,M, Almaz F, Bektaş M. On Helices And Slant Helices in The Lightlike Cone, Honam Mathematical J. 2018; 40(2): pp. 305–314.
  • [13] Kühnel W. Differential Geometry: Curves—Surfaces—Manifolds. Student Mathematical Library, vol. 77. Am. Math. Soc., Providence 2015.
  • [14] Liu H. Curves in the lightlike cone. Beitr. Algebra Geom. 2004; 45(1): 291–303.
  • [15] Liu H. Meng Q. Representation formulas of curves in a two-and three-dimensional lightlike cone. Results Math. 2011; 59(3–4): 437–451.
  • [16] O’Neill B. Semi-Riemannian geometry with applications to relativity. New York: Academic Press 1983.
  • [17] Sun J, Pei D. Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres. J. Nonlinear Sci. Appl. 2015; 8(3): 275–284.
  • [18] Unger DJ. Developable surfaces in elastoplastic fracture mechanics. Int. J. Fract. 1991; 50: 33–38.
There are 18 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section MBD
Authors

Fatma Almaz 0000-0002-1060-7813

Mihriban Külahci 0000-0002-8621-5779

Publication Date September 15, 2021
Submission Date January 31, 2021
Published in Issue Year 2021 Volume: 33 Issue: 2

Cite

APA Almaz, F., & Külahci, M. (2021). ℚ𝟐 𝟑 ⊂ 𝐄𝟐 𝟒 Lightlike Koni 3-Uzayında Null Eğrilerin Elastik Olmayan Akış(İnextensible Flow) Eğrileri. Fırat Üniversitesi Mühendislik Bilimleri Dergisi, 33(2), 667-673. https://doi.org/10.35234/fumbd.871674
AMA Almaz F, Külahci M. ℚ𝟐 𝟑 ⊂ 𝐄𝟐 𝟒 Lightlike Koni 3-Uzayında Null Eğrilerin Elastik Olmayan Akış(İnextensible Flow) Eğrileri. Fırat Üniversitesi Mühendislik Bilimleri Dergisi. September 2021;33(2):667-673. doi:10.35234/fumbd.871674
Chicago Almaz, Fatma, and Mihriban Külahci. “ℚ𝟐 𝟑 ⊂ 𝐄𝟐 𝟒 Lightlike Koni 3-Uzayında Null Eğrilerin Elastik Olmayan Akış(İnextensible Flow) Eğrileri”. Fırat Üniversitesi Mühendislik Bilimleri Dergisi 33, no. 2 (September 2021): 667-73. https://doi.org/10.35234/fumbd.871674.
EndNote Almaz F, Külahci M (September 1, 2021) ℚ𝟐 𝟑 ⊂ 𝐄𝟐 𝟒 Lightlike Koni 3-Uzayında Null Eğrilerin Elastik Olmayan Akış(İnextensible Flow) Eğrileri. Fırat Üniversitesi Mühendislik Bilimleri Dergisi 33 2 667–673.
IEEE F. Almaz and M. Külahci, “ℚ𝟐 𝟑 ⊂ 𝐄𝟐 𝟒 Lightlike Koni 3-Uzayında Null Eğrilerin Elastik Olmayan Akış(İnextensible Flow) Eğrileri”, Fırat Üniversitesi Mühendislik Bilimleri Dergisi, vol. 33, no. 2, pp. 667–673, 2021, doi: 10.35234/fumbd.871674.
ISNAD Almaz, Fatma - Külahci, Mihriban. “ℚ𝟐 𝟑 ⊂ 𝐄𝟐 𝟒 Lightlike Koni 3-Uzayında Null Eğrilerin Elastik Olmayan Akış(İnextensible Flow) Eğrileri”. Fırat Üniversitesi Mühendislik Bilimleri Dergisi 33/2 (September 2021), 667-673. https://doi.org/10.35234/fumbd.871674.
JAMA Almaz F, Külahci M. ℚ𝟐 𝟑 ⊂ 𝐄𝟐 𝟒 Lightlike Koni 3-Uzayında Null Eğrilerin Elastik Olmayan Akış(İnextensible Flow) Eğrileri. Fırat Üniversitesi Mühendislik Bilimleri Dergisi. 2021;33:667–673.
MLA Almaz, Fatma and Mihriban Külahci. “ℚ𝟐 𝟑 ⊂ 𝐄𝟐 𝟒 Lightlike Koni 3-Uzayında Null Eğrilerin Elastik Olmayan Akış(İnextensible Flow) Eğrileri”. Fırat Üniversitesi Mühendislik Bilimleri Dergisi, vol. 33, no. 2, 2021, pp. 667-73, doi:10.35234/fumbd.871674.
Vancouver Almaz F, Külahci M. ℚ𝟐 𝟑 ⊂ 𝐄𝟐 𝟒 Lightlike Koni 3-Uzayında Null Eğrilerin Elastik Olmayan Akış(İnextensible Flow) Eğrileri. Fırat Üniversitesi Mühendislik Bilimleri Dergisi. 2021;33(2):667-73.