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