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 ofconformal maps between equidimensional manifolds.