Details

Rashad A. Abdel-Baky ^[a]

Timelike surfaces with a common asymptotic curve in Minkowski \(3\)-space

Pages: 379-395
Received: 27 December 2016
Accepted in revised form: 21 November 2017
Mathematics Subject Classification (2010): 53B30, 51B20, 53C50.
Keywords: Serret-Frenet formulae, Marching-scale functions, Spacelike and timelike asymptotic curves.

Abstract: In this paper, we study the problem of constructing a timelike surface pencil from a given spacelike or timelike asymptotic curve in Minkowski 3-space \(\mathbb{E}_{1}^{3}\). Using the Serret--Frenet frame of the given spacelike or timelike asymptotic curve, we present the timelike surface as a linear combination of this frame and analyze the necessary and sufficient condition for that curve to be asymptotic. We illustrate this method by presenting some examples.

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