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

Sokur B., Dirim T.

Universal Journal of Mathematics and Applications, vol.6, no.3, pp.114-121, 2023 (Scopus) identifier


In this paper, we study the conchodial surfaces in 3-dimensional Euclidean space with the condition ∆xi = λixi 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.