WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
Quadric Surfaces in Terms of Coordinate Finite II-type
Authors: , , ,
Abstract: 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 $$E^{3}$$. Then, we characterize the coordinate finite type quadrics involving the second fundamental form.
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Keywords: Beltrami-Laplace operator, Quadric Surfaces, Surfaces in the Euclidean 3-space, Surfaces of finite Chen-type, Surfaces of coordinate finite type, Ruled surfaces
Pages: 69-74
DOI: 10.37394/23206.2025.24.9