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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 6 | Year 2022 | Article Id. IJMTT-V68I6P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I6P521

Torsion of a Unit Curve with Constant Angle to its Binormal


Paul Ryan A. Longhas,and Alsafat M. Abdul
Received Revised Accepted Published
09 May 2022 25 Jun 2022 27 Jun 2022 04 Jul 2022
Abstract

In this article, we characterized all unit regular curve with constant angle to its binormal in terms of its torsion. Furthermore, we proved that if 𝛼 is a unit regular curve defined on open interval with constant angle to its Binormal vector, then its torsion is equal to 0. Consequently, we give a condition when the tangent vector 𝑇 of 𝛼 lie in a plane.

Keywords
Torsion, Curve, Binormal, Constant Angle, Curvature.
References

[1] Nguyen T.P, Debled-Rennesson I, “Curvature and Torsion Estimators for 3D Curves, In et al. Advances in Visual Computing, ISVC, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, vol. 5358, 2008.
[2] Thomas Lewiner, João D. Gomes, Hélio Lopes, Marcos Craizer, “Curvature, and Torsion Estimators Based on Parametric Curve Fitting,” Computers & Graphics, vol. 29, no. 5, pp. 641-655, 2005.
[3] Manuel Gonzalez-Espinoza, Giovanni Otalora, LucilaKraiselburd, and Susana Landau, “Parametrized Post-Newtonian Formalism in Higher-Order Teleparallel Gravity,” Journal of Cosmology and Astroparticle Physics, 2022.
[4] Ogievetskij V.I & Sokachev Eh. S, “Torsion and Curvature in Terms of the Axial Superfield,” Nuclear physic, vol. 32, no. 3, pp. 870- 879, 1980.
[5] Dragon N, “Torsion and Curvature in Extended Supergravity,” Z. Phys. C - Particles and Fields, vol. 2, pp. 29–32, 1979.
[6] Peter Baekler and Friedrich W Hehl, “Beyond Einstein–Cartan Gravity: Quadratic Torsion and Curvature Invariants with Even and Odd Parity Including All Boundary Terms,” Class. Quantum Grav. vol. 28, pp. 215017, 2011.
[7] Rainer W. Kuhne, “Gauge Theory of Gravity Requires Massive Torsion Field,” International Journal of Modern Physics A, vol. 14, no. 16, pp. 2531-2535, 1999.
[8] Gammack D & Hydon P, “Flow in Pipes with Non-Uniform Curvature and Torsion,” Journal of Fluid Mechanics, vol. 433, pp. 357- 382, 2001.
[9] Bolinder C, “First- and Higher-Order Effects of Curvature and Torsion on the Flow in a Helical Rectangular Duct,” Journal of Fluid Mechanics, vol. 314, pp. 113-138, 1996.
[10] Betchov R, On the Curvature and Torsion of an Isolated Vortex Filament,” Journal of Fluid Mechanics, vol. 22, no. 3, pp. 471-479, 1965.
[11] J. Maeck and G. De Roeck, “Dynamic Bending and Torsion Stiffness Derivation from Modal Curvature and Torsion Rates,” Journal of Sound and Vibration, vol. 225, no. 1, pp. 153-170, 1999.
[12] Saridakis E, Myrzakul S, Myrzakulov K and Yerzhanov K, “Cosmological Applications of f(r,t) Gravity with Dynamical Curvature and Torsion,” American Physical Society, vol. 102, no. 2, pp. 023525, 2000.
[13] He L, Tan H & Huang ZC, Online Handwritten Signature Verification Based on Association of Curvature and Torsion Feature with Hausdorff Distance,” Multimed Tools Appl, vol. 78, pp. 19253–19278, 2019.
[14] Fang L, Lu W, Huang W, “Estimate Algorithms and Embedded Crafts of Curvature and Torsion,” Journal of Graphics, vol. 33, no. 2, pp. 9–13, 2012.
[15] Pişcoran LI, Mishra V.N,”S-Curvature for a New Class of (Α,Β)-Metrics,” RACSAM, vol. 111, pp. 1187–1200, 2017.
[16] Spivak, Michael, “A Comprehensive Introduction to Differential Geometry,” Publish or Perish, Inc, vol. 2, 1999.
[17] Sternberg, Shlomo, “Lectures on Differential Geometry,” Prentice-Hall, 1964.
[18] Struik, Dirk J, “Lectures on Classical Differential Geometry,” Reading, Mass: Addison-Wesley, 1961.
[19] Kühnel, Wolfgang, “Differential Geometry, Student Mathematical Library," Providence, R.I.: American Mathematical Society, vol. 16, pp. 1882174, 2002.
[20] Hanson A.J, "Quaternion Frenet Frames: Making Optimal Tubes and Ribbons from Curves (PDF),” Indiana University Technical Report, 2007.
[21] Frenet F, “On Double Curvature Curves (PDF), Thesis, Toulouse,” Abstract in Journal of Pure and Applied Mathematics, vol. 17, 1852.
[22] Guggenheimer, Heinrich, “Differential Geometry,” Dover, 1977.
[23] Serret J. A, "On Some Formulas Relating to the Theory of Double Curvature Curves (PDF),” Journal of Pure and Applied Mathematics, vol. 16, 1851.
[24] Jordan, Camille, "On the Theory of Curves in N-Dimensional Space", C. R. Acad. Sci. Paris, vol. 79, pp. 795–797, 1874.
[25] Etgen Garret, Hille Einar, Salas Saturnino, Salas and Hille's “Calculus — One and Several Variables 7th ed.,” John Wiley & Sons, pp. 896, 1995.

Citation :

Paul Ryan A. Longhas,and Alsafat M. Abdul, "Torsion of a Unit Curve with Constant Angle to its Binormal," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 6, pp. 169-172, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I6P521

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