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
Fatma Almaz
,
Mihriban Külahci
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.
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Year 2021,
Volume: 33 Issue: 2, 667 - 673, 15.09.2021
Fatma Almaz
,
Mihriban Külahci
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.
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- [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.
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- [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.
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- [18] Unger DJ. Developable surfaces in elastoplastic fracture mechanics. Int. J. Fract. 1991; 50: 33–38.