Bi-f-harmonic curves on lorentzian para-sasakian manifolds

In this study, which was prepared as a master's thesis, the necessary and sufficient conditions for non-null curves to be non-harmonic (original) bi-f-harmonic curves on 4-dimensional conformal flat, quasi conformal flat or conformal symmetric Lorentzian para-Sasakian manifolds bi-f-harmonic equations of these curves are given. This thesis consists of four chapters. The first part is the introduction part of the thesis and in this part, the previous studies on the development of the research subject are explained. In the second part, definitions and theorems related to harmonic transformations, biharmonic transformations, f-biharmonic transformations and bi-f-harmonic transformations are presented in order to better understand the next sections. In the third chapter, definitions and theorems about semi-Riemannian manifolds and Lorentzian almost paracontact manifolds are given. The original part of the thesis is the fourth chapter, and in this section, theorems related to the conditions of being a bi-f-harmonic of a spacelike and a timelike curve defined on 4-dimensional conformal flat, quasi conformal flat or conformal symmetric Lorentzian para-Sasakian manifolds.