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ON THE CONFORMAL TRIHARMONIC MAPS

  • Ouakkas, Seddik (Laboratory of Geometry, Analysis, Control and Applications University of Saida, Dr Moulay Tahar) ;
  • Reguig, Yasmina (Laboratory of Geometry, Analysis, Control and Applications University of Saida, Dr Moulay Tahar)
  • Received : 2021.03.09
  • Accepted : 2021.10.07
  • Published : 2022.04.30

Abstract

In this paper, we give the necessary and sufficient condition for the conformal mapping ϕ : (ℝn, g0) → (Nn, h) (n ≥ 3) to be triharmonic where we prove that the gradient of its dilation is a solution of a fourth-order elliptic partial differential equation. We construct some examples of triharmonic maps which are not biharmonic and we calculate the trace of the stress-energy tensor associated with the triharmonic maps.

Keywords

Acknowledgement

The authors would like to thank the referee for some useful comments and their helpful suggestions that have improved the quality of this paper.

References

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