TY - EJOU
AU - Çakmak, Ali
AU - Kızıltuğ, Sezai
AU - Mumcu, Gökhan
TI - Notes on Curves at a Constant Distance from the Edge of Regression on a Curve in Galilean 3-Space
T2 - Computer Modeling in Engineering \& Sciences
PY - 2023
VL - 135
IS - 3
SN - 1526-1506
AB - In this paper, we define the curve at a constant distance from the edge of regression on a curve *r*(*s*) with arc length parameter *s* in Galilean 3-space. Here, *d* is a non-isotropic or isotropic vector defined as a vector tightly fastened to Frenet trihedron of the curve *r*(*s*) in 3-dimensional Galilean space. We build the Frenet frame of the constructed curve with respect to two types of the vector *d* and we indicate the properties related to the curvatures of the curve . Also, for the curve , we give the conditions to be a circular helix. Furthermore, we discuss ruled surfaces of type *A* generated via the curve and the vector *D* which is defined as tangent of the curve in 3-dimensional Galilean space. The constructed ruled surfaces also appear in two ways. The first is constructed with the curve and the non-isotropic vector *D*. The second is formed by the curve and the non-isotropic vector *D*. We calculate the distribution parameters of the constructed ruled surfaces and we show that the ruled surfaces are developable. Finally, we provide examples and visuals to back up our research.
KW - Edge of regression; Galilean space; curvature; helix; ruled surface
DO - 10.32604/cmes.2023.024517