TY - JOUR T1 - Biharmonic Curves in Solvable Lie Group AU - Lee, Ji-eun PY - 2025 DA - October Y2 - 2025 DO - 10.36890/iejg.1660936 JF - International Electronic Journal of Geometry JO - Int. Electron. J. Geom. PB - Kazım İlarslan WT - DergiPark SN - 1307-5624 SP - 230 EP - 242 VL - 18 IS - 2 LA - en AB - In this paper, we study biharmonic curves in the solvable Lie group $G(c_1,c_2)$ with Lorentzian metric. In particular, we find biharmonic almost Legendre curves in the solvable Lie group $G(c_1,c_2)$ with Lorentzian metric. KW - Almost Legendre curve KW - biharmonic curve KW - para-$\beta$-Kenmotau manifold KW - solvable Lie group CR - Chen, B. Y., Ishikawa, S.: Biharmonic surfaces in pseudo-Euclidean spaces. Mem. Fac. Sci. Kyushu Univ. Ser. A 45(2) , 323–347 (1991). CR - Cho, J.T., Inoguchi, J., Lee, J.-E.: Biharmonic curves in 3-dimensional Sasakian space form. Ann. Math. Pura Appl. 186 , 685-701 (2007). CR - Hawking, S.W., Ellis, G. F. R. : The large scale structure of space-time. Cambridge Monographs on Mathematical Physics 1. London: Cambridge University Press, 1973. CR - Inoguchi, J.: Submanifolds with harmonic mean curvature vector field in contact 3-manifolds. Coll. Math. 100, 163-179 (2004). CR - Inoguchi, J.: Minimal surfaces in 3-dimensional solvable Lie groups. Chinese Ann. Math. B. 24, 73-84 (2003). CR - Inoguchi, J.: Minimal surfaces in 3-dimensional solvable Lie groups II. Bull. Austral. Math. Soc. 73, 365-374 (2006). CR - Inoguchi, J.: Biharmonic curves in Minkowki 3-space. Int. J. Math. Math. Sci. 2003(21), 1365-1368 (2003). CR - Inoguchi, J., Lee, S.: A Weierstrass representation for minimal surfaces in Sol. Proc. Amer. Math. Soc. 136, 2209-2216 (2008). CR - Inoguchi, J., Lee, J. E.: Slant curves in 3-dimensional almost contact metric geometry. Int. Electron. J. Geom. 8(2), 106–146 (2015). CR - Lee, J. E.: Biharmonic spacelike curves in Lorentzian Heigenberg space. Commun. Korean Math. Soc., 33(4) , 1309–1320 (2018). CR - Lee, J. E.: Biharmonic curves in 3-dimensional Lorentzian Sasakian space forms. Commun. Korean Math. Soc., 35(3) , 967–977 (2020). CR - Lee, J. E.: Pointwise slant curves in pseudo-Hermitian geometry,.Mediterr. J. math. 19, Article number 130 (2022). CR - Sasahara, T.: Biharmonic submanifolds in normalflat Lorentz 3-space forms. Bull. Aust. Math. Soc. 85, 422–432 (2012). CR - Tricerri, F., Vanhecke, L.: Homogeneous Structures on Riemannian Manifolds. Lecture Notes Series, London Math. Soc. 52, Cambridge Univ. Press (1983). CR - Wełyczko, J.: Slant curves in 3-dimensional normal almost paracontact metric manifolds. Mediterr. J. math. 11, 965–978 (2014). CR - Wełyczko, J.: On Legendre curves in 3-dimensional normal almost paracontact metric manifolds. Result. Math. 54, 377-387 (2009). UR - https://doi.org/10.36890/iejg.1660936 L1 - https://dergipark.org.tr/en/download/article-file/4704562 ER -