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

Abstract

Abstract:In this paper, we investigate the parametric representation for a family of surfaces through a given geodesic curve G 3 . We provide necessary and sufficient conditions for this curve to be an isogeodesic curve on the parametric surfaces using Frenet frame in Galilean space. Also, for the sake of visualizing of this study, we plot an example for this surfaces family.

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.…”

“…Here, by taking the T N B 2 -Smarandache curve of ( ) instead of the curve ( ) in (9), let us de…ne a parametric hypersurface ' T N B2 ( ; ; ) which is given with the aid of the T N B 2 -Smarandache curve of ( ) and the Frenet vectors of the curve ( ) as follows If T N B 2 -Smarandache curve of the curve ( ) is a isoparametric curve on a hypersurface ' T N B2 ( ; ; ) in G 4 for = 0 and = 0 ; then from (8), the normal of this hypersurface is…”

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].…”

Interpolation of surfaces with asymptotic curves in Euclidean 3-space

“…This method can be used for obtaining the minimal cost of the material while building surfaces. The family surfaces have been studied for example as in [13,14,1,2,27,28].…”