Erhan Güler, Yusuf Yaylı, Hasan Hilmi Hacısalihoğlu

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We introduce the bi-rotational hypersurface $\mathbf{x(}u,v,w\mathbf{)}$ in the four dimensional Euclidean geometry ${\mathbb{E}}^{4}.$ We obtain the $i$-th curvatures of the hypersurface. Moreover, we consider the Laplace--Beltrami operator of the bi-rotational hypersurface satisfying $ \Delta \mathbf{x=}\mathcal{A}\mathbf{x}$ for some $4\times 4$ matrix $ \mathcal{A}$.


bi-rotational hypersurface, Eucledian geometry, curvative formulas

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