Classification of Surfaces of Finite Chen II-Type

In this paper, we delve into the fascinating realm of quadric surfaces, with a specific focus on those of finite type. We first define relations regarding the first and the second Laplace operators corresponding to the second fundamental form II of a surface in the Euclidean space E 3 . We focus on quadric surfaces from two sides, on one side, we study quadric surfaces of the first kind whose Gauss map N satisfies a relation of the form ΔΙΙn = AN, where A is a square matrix of order 3 and ∆ is the second Laplace operator. On the other side, we study quadric surfaces of the second kind with the same property.