On rotational surfaces in pseudo-Euclidean space ${\mathbb{E}}_t^4$ with pointwise 1-type Gauss map

Abstract

In this work, we study some classes of rotational surfaces in the pseudo-Euclidean space ${\mathbb{E}}_t^4$ with profile curves lying in 2-dimensional planes. First, we determine all such surfaces in the Minkowski 4-space ${\mathbb{E}}_1^4$ with pointwise 1-type Gauss map of the first kind and second kind. Then, we obtain rotational surfaces in ${\mathbb{E}}_2^4$ with zero mean curvature and having pointwise 1--type Gauss map of second kind.