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

Abstract

In this paper, we study general rotational surfaces in $\mathbb E^4$ with pointwise 1-type Gauss map. We consider general rotational surfaces in $\mathbb E^4$ whose meridian curves lie in two-dimensional planes. We firstly obtain all general rotational surfaces in $\mathbb E^4$ with proper pointwise 1-type Gauss map of the first kind. Then we classify minimal rotational surfaces of $\mathbb E^4$ with proper pointwise 1-type Gauss map of the second kind.