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Journals / Politeknik Dergisi / 2021 / Cilt: 24 - Sayı: 2

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

Erhan GÜLER
Pages
517–520
Publication Date
2021-06-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, rotational hypersurfaces in the 4-dimensional Euclidean space are discussed.
📊
Key Findings & Data:In addition, Laplace-Beltrami operator has been defined for 4-dimensional hypersurfaces depending on the first fundamental form.
💡
Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Laplace-Beltrami operator · rotational hypersurface · 4-dimensional Euclidean space

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.

Özet

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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Cite This Article

GÜLER, E. (2021). Rotational Hypersurfaces Satisfying ∆^I R=AR in the Four-Dimensional Euclidean Space. Politeknik Dergisi, Cilt: 24 - Sayı: 2, 517–520. https://ajindex.com/articles/422345

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