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SOME RESULTS ON STABLE f-HARMONIC MAPS

  • Embarka, Remli (Department of Mathematics University Mustapha Stambouli) ;
  • Cherif, Ahmed Mohammed (Department of Mathematics University Mustapha Stambouli)
  • Received : 2017.07.11
  • Accepted : 2017.09.26
  • Published : 2018.07.31

Abstract

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 ${\Delta}^{{\mathbb{S}}^n}(f){\circ}{\varphi}{\leq}0$.

Keywords

harmonic maps;f-harmonic maps;stable f-harmonic maps

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