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In this paper, we prove that any stable $f$-harmonic map from sphere $\mathbb{S}^n$ to Riemannian manifold $(N,h)$ is constant, where $f$ is a smooth positive function on $\mathbb{S}^n\times N$ satisfying one condition with $n>2$. We also prove that any stable $f$-harmonic map $\varphi$ from a compact Riemannian manifold $(M,g)$ to $\mathbb{S}^n$ $(n>2)$ is constant where, in this case, $f$ is a smooth positive function on $M\times\mathbb{S}^n$ satisfying $\Delta^{\mathbb{S}^{n}}(f)\circ\varphi\leq 0$.
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참고문헌 (12)
참고문헌 신청
P. Baird / 2003 / Harmonic morphisms between Riemannian manifolds, London Mathematical Society Monographs. New Series / The Clarendon Press, Oxford University Press :29
R. Caddeo / 2001 / Biharmonic submanifolds of $S^3$ / Internat. J. Math. 12(8):867~876
Ahmed Mohammed Cherif / 2015 / Stable $f$-harmonic maps on sphere / 대한수학회논문집 30(4):471~479
N. Course / 2007 / f-harmonic maps which map the boundary of the domain to one point in the target / New York J. Math. 13:423~435
M. Djaa / 2012 / On the generalized of harmonic and bi-harmonic maps / Int. Electron. J. Geom. 5(1):90~100
R. Caddeo / 2001 / Biharmonic submanifolds of
Ahmed Mohammed Cherif / 2015 / Stable $f$-harmonic maps on sphere / 대한수학회논문집 30(4):471~479
N. Course / 2007 / f-harmonic maps which map the boundary of the domain to one point in the target / New York J. Math. 13:423~435
M. Djaa / 2012 / On the generalized of harmonic and bi-harmonic maps / Int. Electron. J. Geom. 5(1):90~100
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