Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map

The theory of finite type submanifolds was introduced by the first author in late 1970s and it has become a useful tool for investigation submanifolds. Later, P. Piccinni extended notion to maps submanifolds; particular, with Gauss map. Since then, there have been rapid developments type. simplest are those which 1-type. classes such constitute very special interesting families theory.