SOME PROPERTIES OF HARMONIC MAPS FOR FINSLER MANIFOLDS

Abstract. This paper is to study further some properties of harmonic maps between Finsler manifolds. Some rigidity theorems for harmonic maps be-tween Finsler manifolds are given. By introducing the stress-energy tensor of maps between Finsler manifolds, some integral formulas are obtained. Moreover, it is proved that any conformal strongly harmonic map from an n(> 2)-dimensional Finsler manifold to a Finsler manifold must be homo-thetic. Finsler manifolds are the differentiable manifolds with Finsler metrics, which are just Riemannian metrics without quadratic restriction. Harmonic maps be-tween Finsler manifolds are also defined as the critical points of their energy functionals by means of the volume measure induced from the projective spher