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In this paper, we prove that any stable $f$-harmonic map $\psi$ from $\mathbb{S}^2$ to $N$ is a holomorphic or anti-holomorphic map, where $N$ is a K\"ahlerian manifold with non-positive holomorphic bisectional curvature and $f$ is a smooth positive function on the sphere $\mathbb{S}^2$ with $\operatorname{Hess}f\leq0$. We also prove that any stable $f$-harmonic map $\psi$ from sphere $\mathbb{S}^n$ $(n>2)$ to Riemannian manifold $N$ is constant.
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참고문헌 (22)
참고문헌 신청
A. M. Cherif / 2014 / On generalized f-Harmonic morphisms, Comment / Math. Univ. Carolin 55 (1) : 17 ~ 27
J. Eells / 1981 / Maps of minimum energy / J. London Math. Soc 23 (2) : 303 ~ 310
K. Kenmotsu / 1972 / A class of almost contact Riemannian manifolds / Tohoku Math. J 24 : 93 ~ 103
Kaddour Zegga / 2015 / On the f-biharmonic Maps and Submanifolds / Kyungpook Mathematical Journal 55 (1) : 157 ~ 168
M. Ara / 1999 / Geometry of F-harmonic maps / Kodai Math. J 22 (2) : 243 ~ 263
J. Eells / 1981 / Maps of minimum energy / J. London Math. Soc 23 (2) : 303 ~ 310
K. Kenmotsu / 1972 / A class of almost contact Riemannian manifolds / Tohoku Math. J 24 : 93 ~ 103
Kaddour Zegga / 2015 / On the f-biharmonic Maps and Submanifolds / Kyungpook Mathematical Journal 55 (1) : 157 ~ 168
M. Ara / 1999 / Geometry of F-harmonic maps / Kodai Math. J 22 (2) : 243 ~ 263
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