On the conformal triharmonic maps

Seddik Ouakkas; Yasmina Reguig

doi:10.4134/CKMS.c210086

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2022; 37(2): 607-629

Online first article March 29, 2022 Printed April 30, 2022

https://doi.org/10.4134/CKMS.c210086

On the conformal triharmonic maps

Seddik Ouakkas, Yasmina Reguig

University of Saida, Dr Moulay Tahar.; University of Saida, Dr Moulay Tahar.

Abstract

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Abstract

In this paper, we give the necessary and sufficient condition for the conformal mapping $phi :left(mathbb{R}^{n},g_{0}ight)ightarrow left( N^{n},hight)$ ($n geq 3$) 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: Conformal map, harmonic map, biharmonic map, triharmonic map

MSC numbers: Primary 31B30, 58E20, 53C43, 35J48, 35J91