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2013•arXiv (Cornell University)Open access

Surfaces with a common asymptotic curve in Minkowski 3-space

Gulnur Saffak, Ergi̇n Bayram, Emi̇n Kasap

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Abstract

In this paper, we express surfaces parametrically through a given spacelike (timelike) asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and sufficient conditions for the coefficients of the Frenet frame to satisfy both parametric and asymptotic requirements are derived. We also present some interesting examples to show the validity of this study.

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In this paper, we express surfaces parametrically through a given spacelike (timelike) asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and sufficient conditions for the coefficients of the Frenet frame to satisfy both parametric and asymptotic requirements are derived. We also present some interesting examples to show the validity of this study.

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Available abstract

In this paper, we express surfaces parametrically through a given spacelike (timelike) asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and sufficient conditions for the coefficients of the Frenet frame to satisfy both parametric and asymptotic requirements are derived. We also present some interesting examples to show the validity of this study.

Key concepts: Frenet–Serret formulas, Minkowski space, Frame (networking), Parametric statistics, Space (punctuation), Mathematics, Mathematical analysis, Parametric equation

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