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

Authors

ERHAN GÜLER
YUSUF YAYLI
HASAN HİLMİ HACISALİHOĞLU

DOI

10.55730/1300-0098.3261

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 $\mathcal{A}$.

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, ERHAN; YAYLI, YUSUF; and HACISALİHOĞLU, HASAN HİLMİ (2022) "Birotational hypersurface and the second Laplace-Beltrami operator in the four dimensional Euclidean space ${\mathbb{E}}^{4}$," Turkish Journal of Mathematics: Vol. 46: No. 6, Article 9. https://doi.org/10.55730/1300-0098.3261
Available at: https://journals.tubitak.gov.tr/math/vol46/iss6/9