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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2026 / Cilt: 25 Sayı: 3

Some Classifications for Tubular Hypersurfaces Generated by Timelike Curves in Lorentz-Minkowski 4-Space

Lorentz-Minkowski 4-Uzayında Timelike Eğriler Tarafından Oluşturulan Tubular Hiperyüzeyler İçin Bazı Sınıflandırmalar

Ahmet Kazan(MALATYA TURGUT ÖZAL ÜNİVERSİTESİ)0000-0002-1959-6102
Mustafa Altın(BINGOL UNIVERSITY)0000-0001-5544-5910
Pages
483–488
Publication Date
2025-06-10
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AI Summary & Key Takeaways

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

After, we gave some classifications for these hypersurfaces, which have the generalized L_0 1-type Gauss map, the first kind and second kind L_0-pointwise 1-type Gauss map and the L_0-harmonic Gauss map, respectively.

📌 3 Key Takeaways

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Objective & Hypothesis:In this study, we are interested in the linearized operator L_0 of the Gaussian maps of tubular hypersurfaces formed by timelike curves in the 4-dimensional Lorentz-Minkowski space E_1^4.
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Key Findings & Data:In this context, firstly we obtained the L_0 operator of the Gauss maps of the tubular hypersurfaces formed by timelike curves in E_1^4.
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Conclusion & Impact:After, we gave some classifications for these hypersurfaces, which have the generalized L_0 1-type Gauss map, the first kind and second kind L_0-pointwise 1-type Gauss map and the L_0-harmonic Gauss map, respectively.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Doğrusallaştırılmış L_0-operatörü · Gauss dönüşümü · Genelleştirilmiş L_0 1-tipli Gauss dönüşümü

Abstract

In this study, we are interested in the linearized operator L_0 of the Gaussian maps of tubular hypersurfaces formed by timelike curves in the 4-dimensional Lorentz-Minkowski space E_1^4. In this context, firstly we obtained the L_0 operator of the Gauss maps of the tubular hypersurfaces formed by timelike curves in E_1^4. After, we gave some classifications for these hypersurfaces, which have the generalized L_0 1-type Gauss map, the first kind and second kind L_0-pointwise 1-type Gauss map and the L_0-harmonic Gauss map, respectively.

Özet

Bu çalışmada, 4-boyutlu Lorentz-Minkowski uzayı E_1^4’de timelike eğriler tarafından oluşturulan tubular hiperyüzeylerin Gauss dönüşümlerinin doğrusallaştırılmış operatörü L_0 ile ilgilendik. Bu bağlamda ilk olarak, E_1^4’de timelike eğriler tarafından oluşturulan tubular hiperyüzeylerin Gauss dönüşümlerinin L_0 operatörünü elde ettik. Ardından sırasıyla, genelleştirilmiş L_0 1-tipli Gauss dönüşümüne sahip, birinci ve ikinci çeşit L_0-noktasal 1-tipli Gauss dönüşümüne sahip ve L_0-harmonik Gauss dönüşümüne sahip olan bu hiperyüzeyler için bazı sınıflandırmalar verdik.

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Cite This Article

Kazan, A., Altın, M. (2025). Some Classifications for Tubular Hypersurfaces Generated by Timelike Curves in Lorentz-Minkowski 4-Space. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 25 Sayı: 3, 483–488. https://doi.org/10.35414/akufemubid.1475288

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