On $f$-biharmonic and bi-$f$-harmonic Frenet Legendre curves

Abstract

This paper is devoted to study the f-harmonic, f-biharmonic, bi-f-harmonic, biminimal and f-biminimal Frenet Legendre curves in three dimensional normal almost paracontact metric manifolds and to determine the necessary and sufficient conditions for these properties. Besides these, some characterizations for such curves have been defined in particular cases of a three dimensional normal almost paracontact metric manifold and some absence theorems have been obtained.