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Journals / Politeknik Dergisi / 2026 / Cilt: 25 Sayı: 1

Rotational Hypersurfaces in Euclidean 4-Space with Density

Mustafa Altın(BİNGÖL ÜNİVERSİTESİ, BİNGÖL TEKNİK BİLİMLER MESLEK YÜKSEKOKULU)0000-0001-5544-5910
Pages
107–114
Publication Date
2022-03-01
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AI Summary & Key Takeaways

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

Besides, the examples of rotational hypersurfaces are given with the aid of the weighted Gaussian and weighted mean curvatures in E^4 with density.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the Euclidean 4-space with a positive density function e^(x^2+y^2+z^2+t^2 ) is studied.
📊
Key Findings & Data:Firstly, the weighted mean and weighted Gaussian curvature functions of a rotational hypersurface in 4-dimensional Euclidean space with density are obtained.
💡
Conclusion & Impact:Besides, the examples of rotational hypersurfaces are given with the aid of the weighted Gaussian and weighted mean curvatures in E^4 with density.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Rotational hypersurfaces · 4-D Euclidean space with density · weighted mean curvatures

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.

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.

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Cite This Article

Altın, M. (2022). Rotational Hypersurfaces in Euclidean 4-Space with Density. Politeknik Dergisi, Cilt: 25 Sayı: 1, 107–114. https://doi.org/10.2339/politeknik.740513

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