TY - JOUR T1 - On the Spherical Indicatrices of a Timelike Curve as Generalized Helices in Minkowski 3-Space AU - Arfah, Arfah AU - Güner Tuğ, Gül PY - 2022 DA - April Y2 - 2022 JF - Konuralp Journal of Mathematics JO - Konuralp J. Math. PB - Mehmet Zeki SARIKAYA WT - DergiPark SN - 2147-625X SP - 50 EP - 54 VL - 10 IS - 1 LA - en AB - In the present paper, we investigate new properties of the spherical indicatrices of a timelike curve in Minkowski 3-space $\mathbb{E}_1^3$. We focus on the conditions of the spherical indicatrix to be a generalized helix depending on its causal character. We also give some integral equations by defining the axis of the helix in the means of the local frame. KW - Null curves KW - null helices KW - spherical indicatrices KW - Minkowski space CR - [1] Ali A.T., New spherical curves and their spherical indicatrices, Global journal of advance research on classical and modern geometries, 2(1) (2009), 28–38. CR - [2] Arfah A., On causal characterization of spherical indicatrices of timelike curves in Minkowski 3-space, Hagia sophia journal of geometry, 2(2) (2020), 26–37. CR - [3] Bilici, M., Ali, A., On the natural lift curves for the involute spherical indicatrices in Minkowski 3- space, Malaya journal of mathematics, 5 (2017), 407–415. CR - [4] Chung, S.K., A study on spherical indicatrix of space curve in E3, Journal of mathematical education, 20(3) (1982), 23–26. CR - [5] Do Carmo, P.D., Differential Geometry of Curves and Surfaces, Prentice Hall, New Jersey, 1976. CR - [6] Erdogan M., Yilmaz G., Null generalized and slant helices in 4-dimensional Lorentz-Minkowski space, Int. J., Contemp., Math. Sci., 3(23) (2008), 1113–1120. CR - [7] Formiga, J., Romero, C., On the differential geometry of curves in Minkowski space, American Journal of Physics, 74 (2006), 1012–1016. https://doi.org/10.1119/1.2232644. CR - [8] Lipschutz, M.M., Schaum’s outline of differential geometry, McGraw-Hill, Canada, 1969. CR - [9] Liu H., Yuan Y., Pitch functions of ruled surfaces and B-scrolls in Minkowski 3-space, Journal of geometry and physics, 62 (2012), 47–52. CR - [10] Lopez, R., Differential geometry of curves and surface in Lorentz-Minkowski space, International electronic journal of geometry, 1(2) (2014), 44–107. CR - [11] Lucas, A.A., Lambin, P., Diffraction by DNA, carbon nanotubes and other helical nanostructures, Rep. Prog. Phys., 68 (2005), 1181-–1249. CR - [12] Mohajan, H.K., Minkowski geometry and space-time manifold in relativity,Journal of enviromental techniques, 1 (2013), 101–109. CR - [13] O’neil, B., Semi-Riemannian geometry and its applications to relativity, Academic press, New York, 1983. CR - [14] Philips, J., Freedom in machinery, Cambridge University Press, New York, 1990. CR - [15] Qian, J., Liu, J., Tian, X., Kim, Y.H., Structure functions of pseudo null curves in Minkowski 3-space. Mathematics, 8(1) 2020, 75–84. https://doi.org/10.3390/math8010075. CR - [16] Shinkin, E.V., Handbook and atlas of curves, CRC Press, Florida, 1995. CR - [17] Struik, D.J., Lectures on Classical Differential Geometry, 2nd ed., Dover, Mineola, 1988. CR - [18] Synge, J.L., Time-like helices in flat spacetime, Proc. Irish. Acade. A., 65 (1967), 27—42. UR - https://dergipark.org.tr/en/pub/konuralpjournalmath/issue//907252 L1 - https://dergipark.org.tr/en/download/article-file/1675600 ER -