Quadric Surfaces in Terms of Coordinate Finite II-type

Quadric surfaces of finite type are a class of three-dimensional surfaces in geometry that are defined by second-degree equations in three variables, which are an essential part of the study of conic sections, and they exhibit a wide range of interesting geometric properties and real-world applications. This paper explores the intriguing domain of quadric surfaces, particularly emphasizing those of finite type. This will start by defining the ideas of the second Laplace-Beltrami operators, involving a surface's second fundamental form (II) in the Euclidean space E3. Then, we characterize the coordinate finite type quadrics involving the second fundamental form.