Spacelike Surfaces with a Common Line of Curvature in Lorentz-Minkowski 3-Space

This paper aims to study spacelike surfaces from a given spacelike curve in Minkowski 3–space. Also, we investigate the necessary and sufficient conditions for the given space-like curve to be the line of curvature on the space-like surface. Depending on the causal character of the curve, the necessary and sufficient conditions for the given space-like curve to satisfy the line of curvature and the geodesic (resp. asymptotic) requirements are also analyzed. Furthermore, we give with illustration some computational examples in support of our main results.

SURFACE FAMILY WITH COMMON LINE OF CURVATURE IN 3-DIMENSIONAL GALILEAN SPACE

In this paper we study to find parametric presentation of a surface family with common line of curvature in 3-dimensional Galilean space. We obtain necessary and sufficient conditions for the curve to be a common line of curvature on this surface. We state examples to visualize our results and we obtain some results for a torsion free curve.