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

Betül Bulca Sokur; Tuğçe Dirim

doi:10.32323/ujma.1330866

EN

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

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 $v$.

Keywords

Conchoid, Gaussian curvature, Laplace operator, Mean curvature

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Betül Bulca Sokur ^*
0000-0001-5861-0184
Türkiye

Tuğçe Dirim
0000-0001-5893-0401
Türkiye

Early Pub Date

September 21, 2023

Publication Date

September 30, 2023

Submission Date

July 21, 2023

Acceptance Date

September 18, 2023

Published in Issue

Year 2023 Volume: 6 Number: 3

DOI

https://doi.org/10.32323/ujma.1330866

IZ

https://izlik.org/JA95JZ27FY

APA

Bulca Sokur, B., & Dirim, T. (2023). Conchoidal Surfaces in Euclidean 3-space Satisfying $\Delta x_{i}=\lambda _{i}x_{i}$. Universal Journal of Mathematics and Applications, 6(3), 114-121. https://doi.org/10.32323/ujma.1330866

AMA

1.Bulca Sokur B, Dirim T. Conchoidal Surfaces in Euclidean 3-space Satisfying $\Delta x_{i}=\lambda _{i}x_{i}$. Univ. J. Math. Appl. 2023;6(3):114-121. doi:10.32323/ujma.1330866

Chicago

Bulca Sokur, Betül, and Tuğçe Dirim. 2023. “Conchoidal Surfaces in Euclidean 3-Space Satisfying $\Delta X_{i}=\lambda _{i}x_{i}$”. Universal Journal of Mathematics and Applications 6 (3): 114-21. https://doi.org/10.32323/ujma.1330866.

EndNote

Bulca Sokur B, Dirim T (September 1, 2023) Conchoidal Surfaces in Euclidean 3-space Satisfying $\Delta x_{i}=\lambda _{i}x_{i}$. Universal Journal of Mathematics and Applications 6 3 114–121.

IEEE

[1]B. Bulca Sokur and T. Dirim, “Conchoidal Surfaces in Euclidean 3-space Satisfying $\Delta x_{i}=\lambda _{i}x_{i}$”, Univ. J. Math. Appl., vol. 6, no. 3, pp. 114–121, Sept. 2023, doi: 10.32323/ujma.1330866.

ISNAD

Bulca Sokur, Betül - Dirim, Tuğçe. “Conchoidal Surfaces in Euclidean 3-Space Satisfying $\Delta X_{i}=\lambda _{i}x_{i}$”. Universal Journal of Mathematics and Applications 6/3 (September 1, 2023): 114-121. https://doi.org/10.32323/ujma.1330866.

JAMA

1.Bulca Sokur B, Dirim T. Conchoidal Surfaces in Euclidean 3-space Satisfying $\Delta x_{i}=\lambda _{i}x_{i}$. Univ. J. Math. Appl. 2023;6:114–121.

MLA

Bulca Sokur, Betül, and Tuğçe Dirim. “Conchoidal Surfaces in Euclidean 3-Space Satisfying $\Delta X_{i}=\lambda _{i}x_{i}$”. Universal Journal of Mathematics and Applications, vol. 6, no. 3, Sept. 2023, pp. 114-21, doi:10.32323/ujma.1330866.

Vancouver

1.Betül Bulca Sokur, Tuğçe Dirim. Conchoidal Surfaces in Euclidean 3-space Satisfying $\Delta x_{i}=\lambda _{i}x_{i}$. Univ. J. Math. Appl. 2023 Sep. 1;6(3):114-21. doi:10.32323/ujma.1330866