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

Erhan GÜLER

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

Article Details

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

Authors:

Erhan GÜLER

Publisher:

Gazi University

Main Topics:

Applied physics

Journal:

Journal of Polytechnic 2021 Vol.24 Issue 2, pp.517-520

Document Type:

Article

Publication Date:

5/2021

Document Language:

English

Document ID (Org No.):

2000589115

Frequency:

Monthly

eISSN:

2147-9429

DOI:

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

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.

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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.

Article Details

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

Authors: Erhan GÜLER

Publisher: Gazi University

Main Topics: Applied physics

Journal: Journal of Polytechnic 2021 Vol.24 Issue 2, pp.517-520

Document Type: Article

Publication Date: 5/2021

Document Language: English

Document ID (Org No.): 2000589115

Frequency: Monthly

eISSN: 2147-9429

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

Issues

Authors:

Erhan GÜLER

Publisher:

Gazi University

Main Topics:

Applied physics

Journal:

Journal of Polytechnic 2021 Vol.24 Issue 2, pp.517-520

Document Type:

Article

Publication Date:

5/2021

Document Language:

English

Document ID (Org No.):

2000589115

Frequency:

Monthly

eISSN:

2147-9429

DOI:

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