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

Yıl 2021, , 667 - 673, 15.09.2021

Fatma Almaz , Mihriban Külahci

https://doi.org/10.35234/fumbd.871674

Öz

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.

Anahtar Kelimeler

Elastik olmayan akış (inextensible flow), ℚ2 3 ⊂ E2 4 Lightlike koni uzayı, null eğri

Kaynakça

• [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.