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

Year 2023, , 114 - 121, 30.09.2023

Betül Bulca Sokur , Tuğçe Dirim

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

Cited By: 1

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

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