Spacelike Rotational Surfaces of Elliptic, Hyperbolic and Parabolic Types in Minkowski Space E 1 4 ${E^{4}_{1}}$ with Pointwise 1-Type Gauss Map

Abstract

In this paper, we consider a class of spacelike rotational surfaces in Minkowski space \(\mathbb {E}^{4}_{1}\) with 2-dimensional axis. There are three types of rotational surfaces with 2-dimensional axis, called rotational surfaces of elliptic, hyperbolic or parabolic type. We obtain all flat spacelike rotational surfaces of elliptic and hyperbolic types with pointwise 1-type Gauss map. We also determine flat spacelike rotational surface of parabolic type with pointwise 1-type Gauss map of the first kind. Then, we conclude that there exists no flat spacelike rotational surface of parabolic type in \(\mathbb {E}^{4}_{1}\) with pointwise 1-type Gauss map of the second kind.