Some Results of $f$-Harmonic and Bi-$f$-Harmonic Maps with Potential

Abstract

In this note, we characterize the f -harmonic maps and bi-f -harmonic maps with potential. We prove that every bi-f -harmonic map with potential from complete Riemannian manifold, satisfying some conditions is a f -harmonic map with potential. More, we study the case of conformal maps between equidimensional manifolds.