On the conformal triharmonic maps
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In this paper, we give the necessary and sufficient condition for the conformal mapping $\phi :\left(\mathbb{R}^{n},g_{0}\right)\rightarrow \left( N^{n},h\right)$ ($n \geq 3$) 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.
Abstract
In this paper, we give the necessary and sufficient condition for the conformal mapping $\phi :\left(\mathbb{R}^{n},g_{0}\right)\rightarrow \left( N^{n},h\right)$ ($n \geq 3$) 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.
참고문헌 (12)
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