Parametric representation of a surface pencil with a common line of curvature

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

“…Moreover, surface with common geodesic is one of the most important research topics in Differential Geometry. Some more studies and results about surfaces in G 3 have been given in [1][2][3][4].…”

Spacelike developable surfaces through a common line of curvature in Minkowski 3-space

“…Alourdas et al (Alourdas, et al, 1990) studied how to construct a net of lines of curvature on a B-spline surface. In paper (Li, et al, 2011), the authors studied the parametric surface pencils which possess the given curve as the line of curvature. Moreover, the authors further gave an approach to design the developable surface through the given curve as line of curvature in paper (Li, et al, 2013).…”

Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space

“…With the inspiration of work of Wang, Li et.al. [14] changed the characteristic curve from geodesic to line of curvature and defined the surface pencil with a common line of curvature. Recently, in [15] Bayram et.al.…”