Inextensible Flows of Spacelike Curves According to Equiform Frame in 4-dimensional Minkowski Space R41

93b52e06-e35e-4066-bcbe-aa55d21a5dc520210210083024193wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40512720202720201910.37394/23206.2020.19http://wseas.org/wseas/cms.action?id=23185Inextensible Flows of Spacelike Curves According to Equiform Frame in 4-dimensional Minkowski Space R41W. M.MahmoudDepartment of Mathematics Aswan University Faculty of Science Aswan, EGYPTAlaa HassanNoreldeenDepartment of Mathematics Aswan University Faculty of Science Aswan, EGYPTIn this paper, we study inextensible flows of spacelike curves lying fully on a spacelike surface Ω according to equiform frame in 4-dimensional Minkowski space ℝ1 4 . We give necessary and sufficient conditions for this inextensible flows which are expressed as a partial differential equation involving the equiform curvature functions in 4-dimensional Minkowski space ℝ1 4 . Finally we give an application of inextensible flows of spacelike curves in ℝ1 4 .21020212102021683698https://www.wseas.org/multimedia/journals/mathematics/2020/b525106-1359.pdf10.37394/23206.2020.19.75https://www.wseas.org/multimedia/journals/mathematics/2020/b525106-1359.pdf10.4310/jdg/1214448076S. J. Altschuler, M. A. Grayson, Shortening space curves and flow through singularities, J. Differ. Geom., 33 (1992), 283--298.H. S. Abdel-Aziz, M. Khalifa Saad and A. A. Abdel-Salam, Equiform Differential Geometry of curves in Minkowski space-time, arXiv:1501.02283v1 [math.DG] 9 Jan 2015.D. Conte, B. Paternoster, L. Moradi and F. Mohammadi, Construction of exponentially fitted explicit peer methods, International Journal of Circuits, Systems and Signal Processing, pp. 501-506, Volume 13, 2019.Yu. K. Demjanovich, T. O. Evdokimova, O. N. Ivancova, D. M. Lebedinskii, A. Y. Ponomareva, On Wavelet Decomposition of the Singular Splines, International Journal of Circuits, Systems and Signal Processing, pp. 571-579, Volume 14, 2020.M. P. Do Carmo, Differential geometry of curves and surfaces, Prentice Hall, Englewood Cliffs, NJ, 1976.M. Evren Aydin, MahmutErgut, The equiform differential geometry of curves in 4-dimensional galilean space G_4, Stud. Univ. Babes-Bolyai Math.,58 (3) (2013), 399--406.10.4310/jdg/1214439902M. Gage, R. S. Hamilton, The heat equation shrinking convex plane curves, J. Differ. Geom., 23 (1986), 69—9610.4310/jdg/1214441371M. Grayson,The heat equation shrinks embedded plane curves to round points, J. Differ. Geom., 26 (1987), 285--314.H. Gun Bozok, H. Oztekin, Inextensible flows of curves in the equiform geometry of 4-dimensional Galilean space G_4, Facta Universitais, 30 (2) (2015), 209--216.10.1155/2016/6178961R. A. Hussien, S. G. Mohamed, Generated surfaces via inextensible flows of curves in R^3, J. of Applied Math.,(2016), Article ID 6178961, 8 pages http://dx.doi.org/10.1155/2016/617896110.1016/j.aml.2005.02.004D. Y. Kwon, F. C. Park, D. P. Chi, Inextensible flows of curves and develoble surfaces, Applied Math. Letters, 18 (2005), 1156--1162.10.1080/1726037x.2017.1323416T. Korpinar, On Inextensible flows of curves according to alternative moving frame, J. of Dyn. Syst. and Geomet. Theories, 15 (1) (2017), 15--27.10.1142/s1793557118500018T. Korpinar, New inextensible flows of principal normal spherical image, Asian-European Journal of Mathematics, 11 (1) (2018), (14 pages), https://doi.org/10.1142/S179355711850001810.36890/iejg.594497R. Lopez, Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space, International Electronic Journal of Geometry, 7 (1) (2014), 44—10710.1016/j.joems.2017.04.002S. G. Mohamed, Binormal motions of inextensible curves in de-Sitter space S^2,1, J. of the Egy. Math. Soci., 25 (2017), 313--318.B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic press, New York, 1983.S. Yilmaz, M. Turgut, On the Differential Geometry of the curves in Minkowski space-time, Int. J. Contemp. Math. Sci., 3 (7) (2008), 1343--1349.10.4067/s0719-06462014000300002O. G. Yildiz, S. Ersoy, M. Masal, A note on inextensible flows of curvature on oriented surface, CUBO A Math. J., 16 (3) (2014), 11--19.10.1515/math-2016-0071M. Yeneroglu, On new characterization of inextensible flows of pace-like curves in de Sitter space, Open Math., 14 (2016), 946--954.