TY - JOUR T1 - On Spacelike $(1,3)$-Bertrand Curves in $E_{2}^{4}$ AU - Ağırman Aydın, Tuba AU - Kocayiğit, Hüseyin PY - 2021 DA - December JF - Hagia Sophia Journal of Geometry JO - HSJG PB - Salim YÜCE WT - DergiPark SN - 2687-4261 SP - 1 EP - 11 VL - 3 IS - 2 LA - en AB - 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 $E_{2}^{4}$. KW - Semi-Euclidean space KW - spacelike Bertrand curves KW - spacelike (1 KW - 3)-Bertrand curves CR - Nutbourne, A. W., & Martin, R. R. (1988). Differential geometry applied to curve and surface design. Ellis Horwood,Chichester, UK. CR - Matsuda, H., & Yorozu, S. (2003). Notes on Bertrand curves.Yokohama Math. J., 50, 41-58. CR - Pears, L. R. (1935). Bertrand curves in Riemannian space.Journal of the London Mathematical Society,1-10(3), 180-183. CR - Ekmekçi, N., & İlarslan, K. (2001). On Bertrand curves and their characterization.Differential Geometry-DynamicalSystems, 3(2), 17-24. CR - Yilmaz, M. Y., & Bektas ̧, M. (2008). General properties of Bertrand curves in Riemann-Otsuki space. Nonlinear Analysis:Theory, Methods & Applications, 69(10), 3225-3231. CR - Izumiya, S., & Takeuchi, N. (2002). Generic properties of helices and Bertrand curves.Journal of Geometry, 74(1-2),97-109. CR - Babaarslan, M., & Yayli, Y. (2011). The characterizations of constant slope surfaces and Bertrand curves.InternationalJournal of the Physical Sciences, 6(8), 1868-1875. CR - 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. CR - O’Neill, B. (1983). Semi-Riemannian Geometry with applications to relativity. Academic Press Inc., London. CR - 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. CR - Çöken, A. C., & Görgülü A. (2009). On Joachimsthal’s theorems in semi-Euclidean spaces.Nonlinear Analysis: Theory, Methods & Applications, 70(11), 3932-3942. CR - Ersoy, S., & Tosun, M. (2013). Timelike Bertrand curves in Semi-Euclidean space.International Journal of Mathematicsand Statistics, 14, 78-89. CR - Hacısalihoğlu, H. H. (1980). Yüksek Diferansiyel Geometriye Giriş, Fırat Üniversitesi, Fen Fakültesi Yayınları, Elazığ. CR - Lopez, R. (2014). Differential geometry of curves and surfaces in Lorentz Minkowski space.International Electronic Journal of Geometry, 7(1), 44-107. CR - Balgetir, H., Bektas ̧, M., & Erg ̈ut, M. (2004). Bertrand curves for nonnull curves in 3-dimensional Lorentzian space. Hadronic Journal, 27(2), 229-236. CR - 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. UR - https://dergipark.org.tr/tr/pub/hsjg/issue//932031 L1 - https://dergipark.org.tr/tr/download/article-file/1748431 ER -