Parallel Weingarten surface in Euclidean space with density ez

H. Kormali, M. Akyiǧit

In this study, the condition that the ruled surface of φ(u,v) in Euclidean 3-space with density ez is a Weingarten surface has been studied. While this review is being conducted, Q, F, J of φ(u,v) are called structure functions of the ruled surface were used. Furthermore, the mean curvature Hϕ and Gaussian curvature Kϕ of the Weingarten surface were studied. Later on, the relationship between the mean Hrϕ curvature and Gauss curvature Krϕ of this surface, which is the parallel surface φr(u,v) of the Weingarten surface φ(u,v) in Euclidean space with density ez, was investigated. Weingarten surface φr(u,v) condition of the parallel surface of the ruled Weingarten surface in Euclidean space with density ez was examined. 

Tbilisi Mathematical Journal, Special Issue (IECMSA-2019), pp. 87-98