- Universal Journal of Mathematics and Applications
- Cilt: 6 Sayı: 3
- Conchoidal Surfaces in Euclidean 3-space Satisfying $\\Delta x_{i}=\\lambda _{i}x_{i}$
Conchoidal Surfaces in Euclidean 3-space Satisfying $\\Delta x_{i}=\\lambda _{i}x_{i}$
Authors : Betül Bulca Sokur, Tuğçe Dirim
Pages : 114-121
Doi:10.32323/ujma.1330866
View : 32 | Download : 34
Publication Date : 2023-09-30
Article Type : Research
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