Differential Geometry of Rectifying Submanifolds Bang-Yen Chen (Communicated by Kazım ?Ilarslan)

Abstract

A space curve in a Euclidean 3-space E3is called a rectifying curve if its position vector fieldalways lies in its rectifying plane. This notion of rectifying curves was introduced by the authorin [Amer. Math. Monthly 110 (2003), no. 2, 147-152]. In this present article, we introduce andstudy the notion of rectifying submanifolds in Euclidean spaces. In particular, we prove that aEuclidean submanifold is rectifying if and only if the tangential component of its position vectorfield is a concurrent vector field. Moreover, rectifying submanifolds with arbitrary codimensionare completely determined.