Liouville Type Theorems Of Harmonic Maps For Finsler Manifolds

In this paper, we can prove that: (1) Any non-degenerate strongly harmonic map from a compact Finsler manifold with non-negative flag curvature to a Finsler manifold with non-positive flag curvature must be totally geodesic. (2) If (M, F) is a compact Landsberg space with sectional flag curvature, then any non-degenerate strongly harmonic map from (M, F) with non-negative Ricci curvature to a Finsler manifold with non-positive flag curvature must be totally geodesic, which generalizes the result of Eells and Sampson (Amer. J. Math. 86: 106-160, 1964).