On $f$-biharmonic and bi-$f$-harmonic Frenet Legendre curves
Keywords:Frenet Curves, Legendre Curves, Normal Almost Paracontact Metric Manifolds, f-Harmonic Curves, f-Biharmonic Curves, Bi-f-Harmonic Curves, f-Biminimal Curves
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.
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