WSEAS Transactions on Mathematics
Print ISSN: 1109-2769 , E-ISSN: 2224-2880
Volume 24, 2025
Classification of Surfaces of Finite Chen II-Type
Authors: , ,
Abstract: 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 $$Δ^{ΙΙ}n = AN$$, where A is a square matrix of order 3 and Δ is the second Laplace operator. On the other side,
we study quadric surfaces of the second kind with the same property.