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On the f-biharmonic Maps and Submanifolds
Zegga, Kaddour,Cherif, A. Mohamed,Djaa, Mustapha Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.1
In this paper, we prove that every f-biharmonic map from a complete Riemannian manifold into a Riemannian manifold with non-positive sectional curvature,satisfying some condition, is f-harmonic. Also we present some properties for the f-biharmonicity of submanifolds of $\mathbb{S}^n$, and we give the classification of f-biharmonic curves in 3-dimensional sphere.
STABLE f-HARMONIC MAPS ON SPHERE
CHERIF, AHMED MOHAMMED,DJAA, MUSTAPHA,ZEGGA, KADDOUR Korean Mathematical Society 2015 대한수학회논문집 Vol.30 No.4
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 $K{\ddot{a}}hlerian$ manifold with non-positive holomorphic bisectional curvature and f is a smooth positive function on the sphere ${\mathbb{S}}^2$with Hess $f{\leq}0$. We also prove that any stable f-harmonic map ${\psi}$ from sphere ${\mathbb{S}}^n$ (n > 2) to Riemannian manifold N is constant.