Abstract
In this paper, we prove that any stable f-harmonic map <TEX>${\psi}$</TEX> from <TEX>${\mathbb{S}}^2$</TEX> to N is a holomorphic or anti-holomorphic map, where N is a <TEX>$K{\ddot{a}}hlerian$</TEX> manifold with non-positive holomorphic bisectional curvature and f is a smooth positive function on the sphere <TEX>${\mathbb{S}}^2$</TEX>with Hess <TEX>$f{\leq}0$</TEX>. We also prove that any stable f-harmonic map <TEX>${\psi}$</TEX> from sphere <TEX>${\mathbb{S}}^n$</TEX> (n > 2) to Riemannian manifold N is constant.
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