Bi-$f$-Harmonic Legendre Curves on $(\\alpha,\\beta)$-Trans-Sasakian Generalized Sasakian Space Forms

Authors : Şerife Nur Bozdağ, Selcen Yüksel Perktaş, Feyza Esra Erdoğan

Pages : 24-39

Doi:10.53570/jnt.1508392

View : 59 | Download : 41

Publication Date : 2024-09-30

Article Type : Research

Abstract :In this study, we consider bi-$f$-harmonic Legendre curves on $(\\alpha,\\beta)$-trans-Sasakian generalized Sasakian space form. We provide the necessary and sufficient conditions for a Legendre curve to be bi-$f$-harmonic on $(\\alpha,\\beta)$-trans-Sasakian generalized Sasakian space form without any restrictions by a main theorem. Afterward, we investigate these conditions under nine different cases. As a result of these investigations, we obtain the original theorems and corollaries as well as the nonexistence theorems. We perform these investigations according to the $\\rho_{2}$ and $\\rho_{3}$ functions from the curvature tensor of the $(\\alpha,\\beta)$-trans-Sasakian generalized Sasakian space form, the curvature and torsion of the bi-$f$-harmonic Legendre curve, and finally, the positions of the basis vectors relative to each other.
Keywords : Bi-$f$-harmonic curves, Legendre curves, trans-Sasakian space forms, generalized Sasakian space forms