Some types of $f$-biharmonic and bi-$f$-harmonic curves

Abstract

In this paper, we determine necessary and sufficient conditions for a non-Frenet Legendre curve to be $f$-harmonic, $f$-biharmonic, bi-$f$-harmonic, biminimal and $f$-biminimal in three-dimensional normal almost paracontact metric manifold. Besides, we obtain some nonexistence theorems.

Keywords

• non-Frenet Legendre curves
• f-harmonic curves
• f-biharmonic curves
• bi-f-harmonic curves
• biminimal curves
• f-biminimal curves
• normal almost paracontact metric manifolds

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