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

Abstract

In this paper, we obtain the parametric representation for a family of surfaces through a given asymptotic curve by using the Frenet frame in the Galilean space G 3 . Necessary and sufficient conditions are given for that curve to be an isoasymptotic curve on the parametric surfaces. We also provide an example in support of our results.

Hypersurface families with Smarandache curves in Galilean 4-space

“…On the constructions of surface families with common geodesic and asymptotic curves in Galilean Space G 3 and an approach for hypersurface family with common geodesic curve in the Galilean Space G 4 have been handled in [9], [10] and [11], respectively.…”

On the Construction of a Surface Family with Common Geodesic in Galilean Space G3

“…So, we get the functions in (6) and (8) which are general for expressing surfaces with a given curve as an isogeodesic curve in G 3 . Also, different types of these functions can be chosen according to Theorem 3.1.…”

“…The Galilean geometry is one of these geometries whose motions are the Galilean transformations of classical kinematics [5]. There has been a lot of studying about the Differential geometry of the Galilean space G 3 in [6][7][8][9].…”

Surface Family With Common Line of Curvature in 3-Dimensional Galilean Space

“…Curves and surfaces in Galilean geometry has been studied by many authors [3,5,6,[15][16][17]21]. Surfaces family, especially, in Galilean space have been studied in [22][23][24].…”