Conchoidal surfaces in euclidean 3-space satisfying ∆xi = λi xi

Abstract

In this paper, we study the conchodial surfaces in 3-dimensional Euclidean space with the condition ∆xi = λi xi where ∆ 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 give some special cases for the classification theorem by given the radius function r(u, v) with respect to the parameter u and v.