Liouville type theorems of harmonic maps for Finsler manifolds (Q6635804)

It was proven by He-Shen that any non-degenerate strongly harmonic map from a compact Riemannian manifold with non-negative sectional curvature to a Berwald manifold with non-positive flag curvature must be totally geodesic.\N\NIn this work the authors extend this result Finsler manifolds, namely they prove that 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.\N\NThey also show that any non-degenerate strongly harmonic map from a compact Landsberg space with non-negative Ricci curvature to a Finsler manifold with non-positive flag curvature must be totally geodesic.\N\NIn particular any non-degenerate strongly harmonic map from a compact Riemannian manifold with non-negative Ricci curvature to a Finsler manifold with non-positive flag curvature must be totally geodesic.