Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space

Year 2021, Volume: 24 Issue: 2, 517 - 520, 01.06.2021

Erhan Güler

https://doi.org/10.2339/politeknik.670333

Cited By: 5

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

4-dimensional Euclidean space, Laplace-Beltrami operator, rotational hypersurface, curvature

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