Abstract

We consider hypersphere $\mathbf{x}(u,v,w)$ in the four dimensional Euclidean space ${\mathbb{E}}^{4}$. We compute the fourth Laplace-Beltrami operator the hypersphere satisfying $\Delta ^{IV}\mathbf{x=}\mathcal{A} \mathbf{x}$, where $\mathcal{A}\in Mat\left( 4,4\right) $.

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