On the Parallel Surfaces in Galilean Space

Abstract

In this paper, …rst of all, the de…nition of parallel surfaces in Galilean space is given. Then, the relationship between the curvatures of the parallel surfaces in Galilean space is determined. Moreover, the …rst and second fundamental forms of parallel surfaces are found in Galilean space. Consequently, we obtained Gauss curvature and mean curvature of parallel surface in terms of those curvatures of the base surface.

A study of the inextensible flows of tube-like surfaces associated with focal curves in Galilean 3-space G₃

“…Using (2.1) and W = Φ u ∧Φ v , we get the isotropic unit vector δ(u, v) in the tangent plane of the surface as [4] …”

On parallel ruled surfaces in Galilean space

“…Recently, Ünlütürk [11] studied parallel ruled surfaces in Minkowski space. In [3], the authors discussed the parallel surfaces in Galilean space.…”

On a Family of Surfaces with Common Asymptotic Curve in the Galilean space

“…There are several works dealing with this topic. In [2], Dede analyzed tubular surfaces between the Galilean and Euclidean space. Dede et al [3] studied parallel surfaces in the Galilean space.…”

“…In [2], Dede analyzed tubular surfaces between the Galilean and Euclidean space. Dede et al [3] studied parallel surfaces in the Galilean space. Ogrenmis et al [8] obtained characterizations of the helix for a curve in the Galilean space.…”