Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(5): 1569-1578

Printed September 30, 2015

https://doi.org/10.4134/BKMS.2015.52.5.1569

Copyright © The Korean Mathematical Society.

Helicoidal Surfaces of the third fundamental form in Minkowski $3$-space

Miekyung Choi and Dae Won Yoon

Gyeongsang National University, Gyeongsang National University

Abstract

We study helicoidal surfaces with the non-degenerate third fundamental form in Minkowski $3$-space. In particular, we mainly focus on the study of helicoidal surfaces with light-like axis in Minkowski $3$-space. As a result, we classify helicoidal surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form on the surface.

Keywords: helicoidal surfaces, light-like axis, third fundamental form, Minkowski space

MSC numbers: Primary 53A35; Secondary 53B30