The Chen type of conoid surfaces family in Minkowski 3-space $\mathbb{L}^{3}$

Abstract

In this paper, the classification of the conoid surfaces family in Minkowski

3-space $\mathbb{L}^{3}$ is conducted under the condition $\Delta

^{J}r_{i}=\lambda _{i}r_{i}$, $J=I,\;II,\;III,$ where $\lambda _{i}\in

\mathbb{R}$ and $\Delta ^{J}$ denotes the Laplace operator with respect to

the fundamental forms $I,\;II,$ and $III$.