Involute-evolute d-curves in Minkowski 3-space E 3 1
Abstract
In this paper, we examine the notion of the involute-evolute curves for the curves lying the surfaces in Minkowski 3-space E3 1 . We call these new associated curves as involute-evolute and by using the Darboux frame of the curves. We give the representation formulae for spacelike curves in Minkowski 3-space E3 1 and using this formulae we give some characterizations of these curves. Besides, we find the relations between the normal curvatures, the geodesic curvatures and the geodesic torsions of these curves.
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References
As, E., Sarioglugil, A., On the Bishop Curvatures of Involute-Evolute Curve in E3, International Journal of Physical Sciences, 9(7), 140-145, 2014.
Azak, A. Z., Akyigit, M., Ersoy, S., Involute-Evolute Curves in Galilean Space G3 , Department of Mathematics Northwest University, 6(4), 75-80, 2010.
Bektas, O., Yuce, S., Special Involute-Evolute Partner D- curves in E3, European Journal of Pure and Applied Mathematics, 6(1), 20-29, 2013.
Boyer, C., A history of Mathematics, New York Wiley, 1968.
Hacısalihoglu, H. H., Diferensiyel Geometri, Ankara ¨Universitesi Fen Fakultesi, 2000.
Kaya, F. E., On Involute and evolute of the Curve and Curve-Surface pair in Euclidean 3-Space, Pure and Applied Mathematics Journal, 4(1-2), 6-9, 2015.
Kasap, E., Yuce, S., Kuruoglu, N., The Involute-Evolute offsets of Ruled Surfaces, Iranian Journal of Science & Technology, Trans. A, 33(A2), 195-201, 2009.
Ozturk, U., Ozturk, E. B. K., Ilarslan, K., On the Involute-Evolute of the Pseudo null Curve in Minkowski 3-Space, Hindawi Publishing Corporation Journal of App. Math., V.2013, 6pp, 2013.
O’Neill, B., “Semi-Riemannian Geometry with Applications to Relativity”, Academic Press, London, 1983.
Senyurt, S., Altun, Y., Cevahir, C., On the Darboux vector Belonging to Involute Curve a Different View, Mathematical Sciences and Applications E-Notes, 4(2), 131-138, 2016.
Turgut, A., Erdogan, E., Involute-Evolute Curve Couples of Higher Order in Rn and their Horizontal lifts in TRn, Common. Fac. Sci. Univ. Ank. Series A1, 43(3), 125-130, 1992.
Turgut, M., Yilmaz, S., On the Frenet Frame and a Characterization of Space-like Involute-Evolute Curve Couple in Minkowski Space-time, International Mathematical Forum, 3(16), 793-801, 2008.
Turgut, M., Ali, A. T., Lopez-Bonilla, J. L., Time-like Involutes of a spacelike helix in Minkowski Space-time, Apeiron, 17(1), 28-41, 2010.
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