Surface pencil with a common line of curvature in Minkowski 3-space

Abstract

In this paper, we analyze the problem of constructing a surface pencil from a given spacelike (timelike) line of curvature. By using the Frenet frame of the given curve in Minkowski 3-space, we express the surface pencil as a linear combination of this frame and derive the necessary and sufficient conditions for the coefficients to satisfy the line of curvature requirement. To illustrate the method some examples showing members of the surface pencil with their line of curvature are given.Comment: 23 pages, 6 figure

Surface Family With Common Line of Curvature in 3-Dimensional Galilean Space

“…Same authors derived a necessary and sufficient condition for a given curve to be the line of curvature on the surface. Surface family with common line of curvature has been studied in [7,8,12]. Galileo geometry is a type of non-Euclidean geometry based on Galileo principle of relativity [20] and it has many important applications in physics [14].…”

A Surface Family with a Common Asymptotic Null Curve in Minkowski 3-Space E 1 3

“…A lot of works dealing with family of surfaces having a common special curve in both Euclidean space and Minkowski space have been published (see, for instance, [8][9][10][11][12][13]).…”

Surface Family with a Common Natural Asymptotic Lift of a Timelike Curve in Minkowski 3-space

“…presented a constraint for surfaces with a common line of curvature in Minkowski 3-space. In [4][5][6][7][8][9] authors found necessary and sufficient conditions for a given curve to be a common special curve on a surface family in Euclidean and Minkowski spaces. Inspired with the above studies, we find necessary and sufficient condition for a surface family possessing the natural lift of a given timelike curve as a common asymptotic curve.…”

“…In 2014, Ergün et.al. [4] presented a constraint for surfaces with a common line of curvature in Minkowski 3space. In [5 -11] authors found necessary and sufficient conditions for a given curve to be a common special curve on a surface family in Euclidean and Minkowski spaces.…”