STABLE HARMONIC MAPS BETWEEN FINSLER MANIFOLDS AND SSU MANIFOLDS

Using the properties of Cartan tensor, we rewrite the second variation formula for har-monic maps between Finsler manifolds, and we prove that there is no non-degenerate stable harmonic map from a compact SSU manifold to any Finsler manifold, which is obtained by Howard and Wei for the Riemannian case. We also include a proof of a theorem of Shen–Wei which states that there is no non-degenerate stable harmonic map from a compact Finsler manifold to any SSU manifold, by the same second variational formula (see Eq. (2.1) in [Y. B. Shen and S. W. Wei, The stability of harmonic map