On Involute-Evolute Curve Pair in Semi-Euclidean Space

Year 2021, Volume: 13 Issue: 2, 331 - 337, 31.12.2021

Tuba Ağırman Aydın , Hüseyin Kocayiğit

https://doi.org/10.47000/tjmcs.950099

Cited By: 1

Abstract

In this study, a kind of generalized involute and evolute curve pair is considered in 4 dimensional semi Euclidean space with 2 index. The curvatures and the associated Frenet Frame of this kind of generalized
involute-evolute curve pair are presented.

Keywords

Semi-Euclidean space, timelike curves, involute, evolute, curve pairs

References

• [1] Akgun, M., Sivridağ, A.İ., Some characterizations for spacelike inclined curves, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2019), 1576-1585.
• [2] Boyer, C., A History of Mathematics, New York, Wiley, 1968.
• [3] Bükcü, B., Karacan, M.K., On the involute and evolute curves of the timelike curve in Minkowski 3-space, Demonstr. Math., 40(2007), 721–732.
• [4] Çöken, A.C., Görgülü, A., On Joachimsthal’s theorems in semi-Euclidean spaces, Nonlinear Analysis: Theory, Meth. App., 70(2009), 3932–3942.
• [5] Fuchs, D., Evolutes and involutes of spatial curves, Am. Math. Mon., 120(2013), 217–231.
• [6] Hacısalihoğlu, H.H., Yüksek Diferansiyel Geometriye Giriş, Fırat University Publications, Elazı˘g, 1980.
• [7] Hacısalihoglu, H.H., Diferansiyel Geometri, İnönü University Faculty of Arts and Sciences Publications, Malatya, 1983.
• [8] Hanif, M., Hua Hou, Z., Generalized involute and evolute curve-couple in Euclidean space, Int. J. Open Problems Compt. Math., 11(2018), 28–39.
• [9] Hanif, M., Hua Hou Z., Nisar, K.S., On special kinds of involute and evolute curves in 4-dimensional Minkowski space, Symmetry, 10(2018), 317.
• [10] Izumiya, S., Takahashi, M., Spacelike parallels and evolutes in Minkowski pseudo-spheres, Journal of Geometry and Physics 57(2007).
• [11] Millman, R.S., Parker, G.D., Elements of Differential Geometry, Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1977.
• [12] Nolasco, B., Pacheco, R., Evolutes of plane curves and null curves in Minkowski 3-space, J. Geom., 108(2017), 195–214.
• [13] O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity. Academic Press Inc., London, 1983.
• [14] Özyılmaz, E.,Yılmaz, S., Involute-evolute curve couples in the Euclidean 4-Space, Int. J. Open Probl.Compt. Math., 2(2009), 168–174.
• [15] Ersoy, S., Tosun, M., Timelike Bertrand curves in Semi-Euclidean space. Int. J. Math. Stat., 14(2013), 78–89.
• [16] Turgut, A., Erdoğan, E., Involute evolute curve couples of higher order in $R^{n}$ and their horizontal lifts in $R^{n}$, Commun. Fac. Sci. Uni. Ankara, Ser. A, 41(1992), 125–130.