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

Authors : Betül BULCA SOKUR, Tuğçe DİRİM

Pages : 114-121

Doi:10.32323/ujma.1330866

View : 33 | Download : 47

Publication Date : 2023-09-30

Article Type : Research Paper

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 $rinsert ignore into journalissuearticles values(u,v);$ with respect to the parameters $u$ and $v$.
Keywords : Conchoid, Gaussian curvature, Laplace operator, Mean curvature