On Spacelike $(1,3)$-Bertrand Curves in $E_{2}^{4}$

Yıl 2021, Cilt: 3 Sayı: 2, 1 - 11, 27.12.2021

Tuba Ağırman Aydın , Hüseyin Kocayiğit

Öz

In this paper, it is proved that, no special spacelike Frenet curve is a Bertrand curve in $E_{2}^{4}$. Therefore, a generalization of spacelike Bertrand curve is defined and this is called as spacelike $(1,3)$-Bertrand curve in $E_{2}^{4}$. Moreover, the characterizations of spacelike (1,3)-Bertrand curves is given in $E_{2}^{4}$.

Anahtar Kelimeler

Semi-Euclidean space , spacelike Bertrand curves , spacelike (1,3)-Bertrand curves

Kaynakça

• Nutbourne, A. W., & Martin, R. R. (1988). Differential geometry applied to curve and surface design. Ellis Horwood,Chichester, UK.
• Matsuda, H., & Yorozu, S. (2003). Notes on Bertrand curves.Yokohama Math. J., 50, 41-58.
• Pears, L. R. (1935). Bertrand curves in Riemannian space.Journal of the London Mathematical Society,1-10(3), 180-183.
• Ekmekçi, N., & İlarslan, K. (2001). On Bertrand curves and their characterization.Differential Geometry-DynamicalSystems, 3(2), 17-24.
• Yilmaz, M. Y., & Bektas ̧, M. (2008). General properties of Bertrand curves in Riemann-Otsuki space. Nonlinear Analysis:Theory, Methods & Applications, 69(10), 3225-3231.
• Izumiya, S., & Takeuchi, N. (2002). Generic properties of helices and Bertrand curves.Journal of Geometry, 74(1-2),97-109.
• Babaarslan, M., & Yayli, Y. (2011). The characterizations of constant slope surfaces and Bertrand curves.InternationalJournal of the Physical Sciences, 6(8), 1868-1875.
• Uçum, A., Keçilioğlu, O., & İlarslan, K. (2015). Generalized Bertrand curves with timelike (1,3)-normal plane in Minkowskispace-time.Kuwait Journal of Science, 42(3), 10-27.
• O’Neill, B. (1983). Semi-Riemannian Geometry with applications to relativity. Academic Press Inc., London.
• Lucas, P., & Ortega-Yagues, J. A. (2013). Bertrand curves in non-flat 3-dimensional (Riemannian or Lorentzian) spaceforms.Bulletin of the Korean Mathematical Society, 50(4), 1109-1126.
• Çöken, A. C., & Görgülü A. (2009). On Joachimsthal’s theorems in semi-Euclidean spaces.Nonlinear Analysis: Theory, Methods & Applications, 70(11), 3932-3942.
• Ersoy, S., & Tosun, M. (2013). Timelike Bertrand curves in Semi-Euclidean space.International Journal of Mathematicsand Statistics, 14, 78-89.
• Hacısalihoğlu, H. H. (1980). Yüksek Diferansiyel Geometriye Giriş, Fırat Üniversitesi, Fen Fakültesi Yayınları, Elazığ.
• Lopez, R. (2014). Differential geometry of curves and surfaces in Lorentz Minkowski space.International Electronic Journal of Geometry, 7(1), 44-107.
• Balgetir, H., Bektas ̧, M., & Erg ̈ut, M. (2004). Bertrand curves for nonnull curves in 3-dimensional Lorentzian space. Hadronic Journal, 27(2), 229-236.
• İlarslan, K., Kılıc ̧, N. & Erdem, H. A. (2017). Osculating curves in 4-dimensional semi-Euclidean space with index 2.Open Mathematics, 15(1), 562-567.