Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2012; 49(3): 635-645

Printed May 1, 2012

https://doi.org/10.4134/BKMS.2012.49.3.635

Copyright © The Korean Mathematical Society.

A study on a ruled surface with lightlike ruling for a null curve with Cartan frame

N$\dot{\mbox{\sc i}}$hat Ayyildiz and Tunahan Turhan

S\"{u}leyman Demirel University, Sel\c{c}uk University

Abstract

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In this study, we investigate the curvature functions of ruled surface with lightlike ruling for a null curve with Cartan frame in Minkowski 3-space. Also, we give relations between the curvature functions of this ruled surface and curvature functions of central normal surface. Finally, we use the curvature theory of the ruled surface for determine differential properties of a robot end-effector motion.

Keywords: rigid body, null scroll, Cartan frame, Frenet formulae, striction curve

MSC numbers: 53A04, 53A25, 53A40

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