Non linear analysis on manifolds on generalized F-energy variation, between Riemannian manifolds

In this note, we extend the definition of F-harmonic maps [1] and, we give the notion of F-biharmonic maps, which is a generalization of biharmonic maps between Riemannian manifolds [4] and f-biharmonic maps [14] and we discuss some conformal properties and the stability of F-harmonic maps. Also we give a formula to construct some examples of proper F-biharmonic maps. Our results are extensions of [1] and [14].