Helicoidal Surfaces of the third fundamental form in Minkowski $3$-space
Bull. Korean Math. Soc. 2015 Vol. 52, No. 5, 1569-1578
https://doi.org/10.4134/BKMS.2015.52.5.1569
Printed September 30, 2015
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
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