- Politeknik Dergisi
- Vol: 24 Issue: 2
- Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space
Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space
Authors : Erhan GÜLER
Pages : 517-520
Doi:10.2339/politeknik.670333
View : 10 | Download : 3
Publication Date : 2021-06-01
Article Type : Research
Abstract :In this study, rotational hypersurfaces in the 4-dimensional Euclidean space are discussed. Some relations of curvatures of hypersurfaces are given, such as the mean, Gaussian, and their minimality and flatness. In addition, Laplace-Beltrami operator has been defined for 4-dimensional hypersurfaces depending on the first fundamental form. Moreover, it is shown that each element of the 4×4 order matrix A, which satisfies the condition ∆^I R=AR, is zero, that is, the rotational hypersurface R is minimal.Keywords : Laplace-Beltrami operator, rotational hypersurface, 4-dimensional Euclidean space, curvature