Dergiler / Politeknik Dergisi / 2022 / Cilt: 25 - Sayı: 1
Rotational Hypersurfaces in Euclidean 4-Space with Density
- Dergi
- Politeknik Dergisi
- Sayfa
- 107–114
- DOI
- —
Özet
In this paper, the Euclidean 4-space with a positive density function e^(x^2+y^2+z^2+t^2 ) is studied. Firstly, the weighted mean and weighted Gaussian curvature functions of a rotational hypersurface in 4-dimensional Euclidean space with density are obtained. The rotational hypersurfaces are constructed by solving these obtained functions which are second-order non-linear ordinary differential equations. Besides, the examples of rotational hypersurfaces are given with the aid of the weighted Gaussian and weighted mean curvatures in E^4 with density.
Abstract
In this paper, the Euclidean 4-space with a positive density function e^(x^2+y^2+z^2+t^2 ) is studied. Firstly, the weighted mean and weighted Gaussian curvature functions of a rotational hypersurface in 4-dimensional Euclidean space with density are obtained. The rotational hypersurfaces are constructed by solving these obtained functions which are second-order non-linear ordinary differential equations. Besides, the examples of rotational hypersurfaces are given with the aid of the weighted Gaussian and weighted mean curvatures in E^4 with density.