Abstract
Abstract We study some properties of harmonic maps for Finsler manifolds and present two theorems: (1) every non-degenerate harmonic map ϕ from a compact Riemannian manifold with nonnegative Ricci curvature to a Berwald manifold with non-positive flag curvature is totally geodesic; this improves a result of He and Shen [3]. (2) Let M be a compact Riemannian manifold with non-negative Ricci curvature and let M‾ be a complete Finsler manifold with non-positive flag curvature. Then every non-degenerate smooth map ϕ : M → M with trb▽̃dϕ = 0 is totally geodesic; this generalizes a result of Eells and Sampson [2] from the Riemannian case to the Finsler case.
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