Flat surfaces in the Minkowski space $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map

Abstract

In this article, we obtain all nonplanar cylindrical surfaces in the Minkowski space $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind. We also prove that right circular cones and hyperbolic cones in $Bbb{E}_{1}^{3}$ are the only cones in $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind. We conclude that there is notangent developable surface fully lying in $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind.