Abstract
In this paper, we investigate n-dimensional immersed compact sub manifold M of a Euclidean space Rn+p, with the immersion psi : M -> Rn+p, where the tangential component psi(T) of psi is a conformal vector field. A characterization of n-sphere in the Euclidean space Rn+p is obtained. Also conditions under which psi(T) is a conformal vector field in the general case and those in the special case where the submanifold has flat normal connection and p = 2 are obtained as well.