Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space

Güler, Erhan

doi:10.2339/politeknik.670333

Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space

Erhan GÜLER (Bartın Üniversitesi, Fen Fakültesi, Matematik Bölümü, 74100 Bartın, Türkiye)

Politeknik Dergisi

2 0

Yıl: 2021 Cilt: 24 Sayı: 2 Sayfa Aralığı: 517 - 520 Metin Dili: İngilizce DOI: 10.2339/politeknik.670333 İndeks Tarihi: 18-06-2021

Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space

Öz:

In this study, rotational hypersurfaces in the 4-dimensional Euclidean space are discussed. Some relations of curvatures ofhypersurfaces are given, such as the mean, Gaussian, and their minimality and flatness. In addition, Laplace-Beltrami operator hasbeen defined for 4-dimensional hypersurfaces depending on the first fundamental form. Moreover, it is shown that each elementof the 4 × 4 order matrix 𝐀, which satisfies the condition ∆𝐼𝐑 = 𝐀𝐑, is zero, that is, the rotational hypersurface 𝐑 is minimal.

Anahtar Kelime:

Dört-Boyutlu Öklid Uzayında ∆ 𝐼𝐑 = 𝐀𝐑 Koşulunu Sağlayan Dönel Hiperyüzeyler

Öz:

Bu çalışmada, 4-boyutlu Öklid uzayındaki dönel hiperyüzeyler ele alınmıştır. Hiperyüzeylerin ortalama, Gauss eğrilikleri hesaplanıp aralarındaki minimal ve düzlemsel olma durumları gibi bazı bağıntılar verilmiştir. Ayrıca, 4-boyutlu hiperyüzeyler için birinci temel forma bağlı olarak Laplace-Beltrami operatörü tanımlanmıştır. Üstelik, dönel yüzeyin ∆ 𝐼𝐑 = 𝐀𝐑 koşulunu sağlayan 4 × 4 mertebeli 𝐀 matrisinin her elemanının sıfır olduğu, yani 𝐑 dönel hiperyüzeyinin minimal olduğu gösterildi.

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	Güler E (2021). Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space. , 517 - 520. 10.2339/politeknik.670333
Chicago	Güler Erhan Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space. (2021): 517 - 520. 10.2339/politeknik.670333
MLA	Güler Erhan Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space. , 2021, ss.517 - 520. 10.2339/politeknik.670333
AMA	Güler E Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space. . 2021; 517 - 520. 10.2339/politeknik.670333
Vancouver	Güler E Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space. . 2021; 517 - 520. 10.2339/politeknik.670333
IEEE	Güler E "Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space." , ss.517 - 520, 2021. 10.2339/politeknik.670333
ISNAD	Güler, Erhan. "Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space". (2021), 517-520. https://doi.org/10.2339/politeknik.670333

APA	Güler E (2021). Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space. Politeknik Dergisi, 24(2), 517 - 520. 10.2339/politeknik.670333
Chicago	Güler Erhan Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space. Politeknik Dergisi 24, no.2 (2021): 517 - 520. 10.2339/politeknik.670333
MLA	Güler Erhan Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space. Politeknik Dergisi, vol.24, no.2, 2021, ss.517 - 520. 10.2339/politeknik.670333
AMA	Güler E Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space. Politeknik Dergisi. 2021; 24(2): 517 - 520. 10.2339/politeknik.670333
Vancouver	Güler E Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space. Politeknik Dergisi. 2021; 24(2): 517 - 520. 10.2339/politeknik.670333
IEEE	Güler E "Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space." Politeknik Dergisi, 24, ss.517 - 520, 2021. 10.2339/politeknik.670333
ISNAD	Güler, Erhan. "Rotational hypersurfaces satisfying ∆ 𝑰𝐑 = 𝐀𝐑 in the four-dimensional Euclidean space". Politeknik Dergisi 24/2 (2021), 517-520. https://doi.org/10.2339/politeknik.670333