Turkish Journal of Mathematics
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 $\Delta ^{II}\mathbf{x=}\mathcal{A}% \mathbf{x}$ for some $4\times 4$ matrix $\mathcal{A}$.
DOI
10.55730/1300-0098.3261
Keywords
Euclidean spaces, four space, birotational hypersurface, Gauss map, $i$-th curvature, second Laplace-Beltrami operator
First Page
2167
Last Page
2177
Recommended Citation
GÜLER, E, YAYLI, Y, & HACISALİHOĞLU, H. H (2022). Birotational hypersurface and the second Laplace-Beltrami operator in the four dimensional Euclidean space ${\mathbb{E}}^{4}$. Turkish Journal of Mathematics 46 (6): 2167-2177. https://doi.org/10.55730/1300-0098.3261
