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Journals / Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi / 2020 / Cilt: 22 - Sayı: 64

The Characterizations of the Spherical Images of Timelike W-Curves in Minkowski Space-Time

Minkowski Uzay-Zamanda Timelike W-Eğrilerin Küresel Göstergelerinin Karakterizasyonları

Yasin ÜNLÜTÜRK
Muradiye ÇİMDİKER
Süha YILMAZ
Pages
59–66
Publication Date
2022-10-15
DOI
—
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AI Summary & Key Takeaways

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

Finally, we have given some characterizations of the sphericalimage in the case of being helix for the timelike 𝑊 −curve in Minkowski space-time 𝐸14

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We know that 𝑊 −curve is a curve which has constant Frenet curvatures.
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Key Findings & Data:In this study, firstly, wehave investigated the principal normal and binormal spherical images of a timelike 𝑊 −curve onpseudohyperbolic space ℍ03in Minkowski space-time 𝐸14.
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Conclusion & Impact:Finally, we have given some characterizations of the sphericalimage in the case of being helix for the timelike 𝑊 −curve in Minkowski space-time 𝐸14
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

We know that 𝑊 −curve is a curve which has constant Frenet curvatures. In this study, firstly, wehave investigated the principal normal and binormal spherical images of a timelike 𝑊 −curve onpseudohyperbolic space ℍ03in Minkowski space-time 𝐸14. Besides, the binormal spherical image ofthe timelike 𝑊 −curve is a spacelike curve which lies on pseudohyperbolic space ℍ03. Hence, we haveobtained the Frenet-Serret invariants of the mentioned image curve in terms of the invariants of thetimelike W-curve in the same space. Finally, we have given some characterizations of the sphericalimage in the case of being helix for the timelike 𝑊 −curve in Minkowski space-time 𝐸14

Özet

𝑊 −eğrisinin sabit Frenet eğriliklerine sahip bir eğri olduğunu biliyoruz. Bu çalışmada, öncelikle, 𝐸1 4 Minkowski uzay-zamanında, ℍ0 3 pseudohiperbolik uzay üzerinde bir timelike 𝑊 −eğrisinin asli normal ve binormal küresel göstergelerini araştırdık. Yanısıra, ℍ0 3 pseudohiperbolik uzay üzerinde yatan timelike 𝑊 −eğrisinin binormal küresel göstergesi spacelike bir eğridir. Bu nedenle, aynı uzayda, söz konusu görüntü eğrisinin Frenet-Serret değişmezlerini timelike 𝑊 −eğrisinin değişmezleri cinsinden elde ettik. Son olarak, 𝐸1 4 Minkowski uzay-zamanındaki timelike 𝑊 −eğrisi için helis olması durumunda küresel göstergenin bazı karakterizasyonlarını verdik

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Cite This Article

ÜNLÜTÜRK, Y., ÇİMDİKER, M., YILMAZ, S. (2022). The Characterizations of the Spherical Images of Timelike W-Curves in Minkowski Space-Time. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, Cilt: 22 - Sayı: 64, 59–66. https://ajindex.com/articles/491389

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