On parallel ruled surfaces in Galilean space

Abstract

Abstract. In this paper, we investigate the parallel surfaces of the ruled surfaces in Galilean space. There are three types of ruled surfaces in Galilean space. We derive the necessary conditions for each type of the ruled surfaces of the parallel surfaces to be ruled. Consequently, we construct some examples.

k-Kinematik Yüzeyler İçin Konjuge Tanjant Vektörler, Asimptotik Doğrultular, Euler Teoremi ve Dupin Göstergesi

“…Substituting (10), (11), (12) and (13) into (7) completes the proof. [20] D. Sağlam and Ö. Kalkan, "Conjugate tangent vectors and asymptotic directions for surfaces at a constant distance from edge of regression on a surface in…”

“…Mathematicians have written many articles and books by investigating surfaces as Euclidean and non-Euclidean. For these studies, one can read [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] . Eisenhart defined parallel surfaces and their some properties in his book [3].…”

Helicoidal Surfaces in Galilean Space With Density

“…In this part, we give a brief review of curves and surfaces in the Galilean space G 3 . For more details, one can see [12,[14][15][16]18].…”

Surfaces of Revolution with Vanishing Curvature in Galilean 3-Space

“…The geometry of this non-Euclidean space was first studied intensively by Röschel [11]. In the last decade, this space was used by several researchers as an ambient space for the well-known Euclidean concepts (see [2,3,7,9,10] for more examples on special surfaces). The study of the surfaces in the Galilean 3-space can also be found in [1].…”