The development of rectifying submanifolds

In this paper we will review the recent development of rectifying submanifolds, first starting with rectifying curves in E3 in 2003 by B.-Y. Chen. He provided several characterizations and explicit formula for a space rectifying curve [1]. Then, in 2016, he extended the idea of rectifying curves to rectifying submanifold in the higher dimensional Euclidean spaces En [2] and after a year later he defined rectifying submanifold in pseudo-Euclidean spaces Emi [9]. The notion of rectifying submanifold in an arbitrary Riemannian manifolds was introduced associated with torqued vector fields [3] along with some applications and related results [4], [16]. At the end, a weaker version of rectifying submanifold in a Riemannian manifold was introduced with some properties.