Type-1 interpolating sesqui-f-harmonic maps between Riemannian manifolds

Abstract

In this paper, first, we introduce and study a new map called a type-1 interpolating sesqui-$f$-harmonic map. Then, we provide necessary and sufficient conditions for a differentiable curve in a Riemannian space form to be a type-1 interpolating sesqui-$f$-harmonic. These conditions are presented in a main theorem and investigated in several subcases. Moreover, we analyze type-1 interpolating sesqui-$f$-harmonic curves on $S^{n}(1)$ and $H^{n}(-1)$.