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Journals / Universal Journal of Mathematics and Applications / 2023 / Cilt: 6 Sayı: 3

Conchoidal Surfaces in Euclidean 3-space Satisfying $\Delta x_{i}=\lambda _{i}x_{i}$

Betül BULCA SOKUR
Tuğçe DİRİM
Pages
114–121
Publication Date
2023-09-30
DOI
—
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AI Summary & Key Takeaways

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

Furthermore, we have given some special cases for the classification theorem by giving the radius function $r(u,v)$ with respect to the parameters $u$ and $v$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study the conchodial surfaces in 3-dimensional Euclidean space with the condition $\Delta x_{i}=\lambda _{i}x_{i}$ where $\Delta $ denotes the Laplace operator with respect to the first fundamental form.
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Key Findings & Data:We obtain the classification theorem for these surfaces satisfying under this condition.
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Conclusion & Impact:Furthermore, we have given some special cases for the classification theorem by giving the radius function $r(u,v)$ with respect to the parameters $u$ and $v$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Conchoid · Gaussian curvature · Laplace operator

Abstract

In this paper, we study the conchodial surfaces in 3-dimensional Euclidean space with the condition $\Delta x_{i}=\lambda _{i}x_{i}$ where $\Delta $ denotes the Laplace operator with respect to the first fundamental form. We obtain the classification theorem for these surfaces satisfying under this condition. Furthermore, we have given some special cases for the classification theorem by giving the radius function $r(u,v)$ with respect to the parameters $u$ and $v$.

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Cite This Article

SOKUR, B. B., DİRİM, T. (2023). Conchoidal Surfaces in Euclidean 3-space Satisfying $\Delta x_{i}=\lambda _{i}x_{i}$. Universal Journal of Mathematics and Applications, Cilt: 6 Sayı: 3, 114–121. https://ajindex.com/articles/965498

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