When the differentiable curve, used throughoutthis paper, is specifically replaced to the unit speed curve then it is seen that the results coincide with the study [4].In addition we elucidate the characterizations of helix as an example.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we investigate the conditions of being an harmonic curve and research differential equations characterizing any differentiable curve in Euclidean 3-space.
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Key Findings & Data:By means of the Laplacian image of the meancurvature vector field of a curve, it is stated which type of harmonic the curve is.
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Conclusion & Impact:When the differentiable curve, used throughoutthis paper, is specifically replaced to the unit speed curve then it is seen that the results coincide with the study [4].In addition we elucidate the characterizations of helix as an example.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, we investigate the conditions of being an harmonic curve and research differential equations characterizing any differentiable curve in Euclidean 3-space. By means of the Laplacian image of the meancurvature vector field of a curve, it is stated which type of harmonic the curve is. Then we write the theorems relatedto the characterization of the curves and proved these theorems. When the differentiable curve, used throughoutthis paper, is specifically replaced to the unit speed curve then it is seen that the results coincide with the study [4].In addition we elucidate the characterizations of helix as an example.
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Cite This Article
Şenyurt, S., Çakır, O. (2022). Characterizations of Curves According to Frenet Frame in Euclidean 3-Space. Turkish Journal of Mathematics and Computer Science, Cilt: 11 - Sayı: 1, 48–52. https://ajindex.com/articles/609120
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