Conoid Surfaces Family in Three-Dimensional Euclidean Space

Abstract

In this research, we investigate a specific family of conoid surfaces within the three-dimensional Euclidean space E3. We consider the differential geometry of the family. We determine the curvatures of these particular surfaces. Moreover, we provide the necessary conditions for minimality within this framework. Additionally, we compute the Laplace−Beltrami operator for this family and present an example.