Conoid Surfaces Family in Minkowski 3-Space

Abstract

This study focuses on exploring a distinct family of conoid surfaces in the three-dimensional Minkowski space L3. Our main objective is to delve into the differential geometry of this family, analyzing its curvatures in detail. Furthermore, we establish the essential conditions for achieving minimality within this specific framework. Additionally, we calculate the Laplace−Beltrami operator for this family of surfaces and illustrate our findings through an example.