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Paper's Title:

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


M.K. Saad, A.Z. Ansari, M. Akram and F. Alharbi

Department of Mathematics ,
Faculty of Science,
Islamic University of Madinah,


In this paper, we analyze the problem of constructing a timelike surface family from a given non-null curve line of curvature. Using the Frenet frame of the non-null curve in Minkowski space E13  we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for the coefficients to satisfy both the line of curvature and the isoparametric requirements. In addition, a necessary and sufficient condition for the given non-null curve to satisfy the line of curvature and the geodesic requirements is investigated. The extension to timelike surfaces of revolution is also outlined. Meanwhile, some representative non-null curves are chosen to construct the corresponding timelike surfaces which possessing these curves as lines of curvature. Results presented in this paper have applications in geometric modeling and the manufacturing of products. In addition, some computational examples are given and plotted.

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