Rotational Hypersurfaces in Euclidean 4-Space with Density

Year 2022, , 107 - 114, 01.03.2022

Mustafa Altın

https://doi.org/10.2339/politeknik.740513

Cited By: 3

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.

Keywords

Rotational hypersurfaces, Euclidean 4-space with density, weighted mean curvatures, weighted Gaussian curvatures

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