Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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
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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.

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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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