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Journals / Avrupa Bilim ve Teknoloji Dergisi / 2022 / Sayı: 38

Hypersurfaces Families with Common Non-Null Isoasymptotic Curve in Lorentz Minkowski 4-Space

4-Boyutlu Lorentz Minkowski Uzayında Null Olmayan Ortak İzoasimptotik Eğrili Hiperyüzey Aileleri

Çiğdem TURAN
Mustafa ALTIN
Hacı Bayram KARADAĞ
Pages
99–109
Publication Date
2022-08-31
DOI
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AI Summary & Key Takeaways

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

Finally, the study was supported with examples and the graphics were drawn using certain projection methods.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, the parametric equation of hypersurfaces passing through the spacelike and timelike curves that has non-null Frenet vectors in E_1^4 Lorentz Minkowski space was expressed with the help of this curve is Frenet frame.
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Key Findings & Data:Furthermore, hypersurface families were created by giving necessary and sufficient conditions so that the spacelike and timelike curves on E_1^4 is common isoasymptotic on the hypersurface.
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Conclusion & Impact:Finally, the study was supported with examples and the graphics were drawn using certain projection methods.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:4-Boyutlu Lorentz Minkowski Uzayı · Spacelike ve Timelike İzoasimptotik Eğri · Hiperyüzey Aileleri

Abstract

In this study, the parametric equation of hypersurfaces passing through the spacelike and timelike curves that has non-null Frenet vectors in E_1^4 Lorentz Minkowski space was expressed with the help of this curve is Frenet frame. Furthermore, hypersurface families were created by giving necessary and sufficient conditions so that the spacelike and timelike curves on E_1^4 is common isoasymptotic on the hypersurface. Then, these conditions obtained with the help of deviation marching-scale functions were simplified. Finally, the study was supported with examples and the graphics were drawn using certain projection methods.

Özet

Bu çalışmada, E_^4 Lorentz Minkowski uzayında null olmayan Frenet vektörlere sahip spacelike ve timelike eğrilerinden geçen hiperyüzeylerin parametrik denklemi, bu eğrinin Frenet çatısı yardımıyla ifade edildi. Ayrıca E_^4 de spacelike ve timelike eğrilerinin hiperyüzey üzerinde ortak izoasimptotik olması için gerekli ve yeterli koşullar verilerek hiperyüzey aileleri oluşturuldu. Daha sonra sapma fonksiyonları yardımıyla elde edilen bu koşullar sadeleştirildi. Son olarak, örneklerle çalışma desteklendi ve belli izdüşüm metodları kullanılarak örneklerin grafikleri çizildi.

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Cite This Article

TURAN, Ç., ALTIN, M., KARADAĞ, H. B. (2022). Hypersurfaces Families with Common Non-Null Isoasymptotic Curve in Lorentz Minkowski 4-Space. Avrupa Bilim ve Teknoloji Dergisi, Sayı: 38, 99–109. https://ajindex.com/articles/857437

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