Differential geometry of rectifying submanifolds

A space curve in a Euclidean 3-space E^3 is called a rectifying curve if its position vector field always lies in its rectifying plane. This notion of rectifying curves was introduced by the author in [1]. In this present article, we introduce and study the notion of rectifying submanifolds in Euclidean spaces. In particular, we prove that a Euclidean submanifold is rectifying if and only if the tangential component of its position vector field is a eş zamanlı vector field. Moreover, rectifying submanifolds with arbitrary codimension are completely determined.