Birotational hypersurface and the second Laplace-Beltrami operator in the four dimensional Euclidean space ${\mathbb{E}}^{4}$

Source abstract

We consider the birotational hypersurface $\mathbf{x(}u,v,w\mathbf{)}$ with the second Laplace-Beltrami operator in the four dimensional Euclidean space ${\mathbb{E}}^{4}.$ We give the $i$-th curvatures of $\mathbf{x}$. In addition, we compute the second Laplace-Beltrami operator of the birotational hypersurface satisfying $\Delta ^{II}\mathbf{x=}\mathcal{A}$ for some $4\times 4$ matrix $\mathcal{A}$.