Gauss Maps of Ruled Submanifolds and Applications II

Source abstract

The notion of pointwise $1$-type Gauss map was derived from the ordinary finite type Gauss map and it gives an interesting geometric properties on surfaces of $3$-dimensional Euclidean space. In particular, the helicoid and the right cone of $3$-dimensional Euclidean space are characterized by pointwise $1$-type Gauss map. Inspired by such a study, in this paper, we completely classify ruled submanifolds of Euclidean space with pointwise $1$-type Gauss map.