Liouville theorems for $F$-harmonic maps with potential

Abstract

In this paper, we consider the Liouville properties for $F$-harmonic map with potential $H$ from $m$-dimensional complete Riemannian manifold $M$ into any $n$-dimensional Riemannian manifold $N$. By using the stress-energy tensor with potential, we obtain monotonicity formula and prove the non-existence of a non-constant $F$-harmonic map with potential from complete non-compact manifolds on which some certain restrictions about curvatures and potential $H$ are assumed. As the results, we obtain the Liouville type results for an $F$-harmonic map with potential $H$. Our results generalize previous results since we have no degree assumption about the function $F$.