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Journals / Journal of Universal Mathematics / 2024 / Cilt: 7 Sayı: To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI" Özel Sayı

GEOMETRIC PHASES, MAGNETIC CURVES FOR DARBOUX FRAMES ON LIGHTLIKE AND TIMELIKE SURFACES

Şerife Nevin Gürbüz(ESKISEHIR OSMANGAZI UNIVERSITY)0000-0003-3959-1779
Pages
158–174
Publication Date
2024-12-29
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AI Summary & Key Takeaways

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

Finally, we obtain μ,U-magnetic curves in the μ,U-lines direction for 1GDF on lightlike surfaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we obtain ^{ND}E_{T} for null Darboux frame on timelike surface and derive V-magnetic curves for null Darboux frame on a timelike surface in the T-lines direction.
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Key Findings & Data:Also, we present ^{¹GD}E_{T}, ^{^{²GD}}E_{T} for 1GDF, 2GDF on lightlike surfaces in the tangential direction.
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Conclusion & Impact:Finally, we obtain μ,U-magnetic curves in the μ,U-lines direction for 1GDF on lightlike surfaces.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Geometric phase · Darboux frame · magnetic curves

Abstract

In this paper, we obtain ^{ND}E_{T} for null Darboux frame on timelike surface and derive V-magnetic curves for null Darboux frame on a timelike surface in the T-lines direction. Also, we present ^{¹GD}E_{T}, ^{^{²GD}}E_{T} for 1GDF, 2GDF on lightlike surfaces in the tangential direction. Later, we present μ, U-magnetic curves for 1GDF on lightlike surfaces in the T-lines direction. We obtain geometric phase in μ-lines direction for 1GDF on lightlike surface. Finally, we obtain μ,U-magnetic curves in the μ,U-lines direction for 1GDF on lightlike surfaces.

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Cite This Article

Gürbüz, Ş. N. (2024). GEOMETRIC PHASES, MAGNETIC CURVES FOR DARBOUX FRAMES ON LIGHTLIKE AND TIMELIKE SURFACES. Journal of Universal Mathematics, Cilt: 7 Sayı: To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI" Özel Sayı, 158–174. https://doi.org/10.33773/jum.1558660

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