COMPACT SUBMANIFOLDS IN A EUCLIDEAN SPACE

摘要

In this paper we study n-dimensional compact immersed submanifold M of a Euclidean space (R~(n+p), <,>) with the immersion ψ : M → R~(n+p) under the restriction that the tangential component ψ~T of the position vector vector field ψ is a conformal vector field and find a characterization of a n-sphere in the Euclidean space R~(n+p). We also find a condition under which the vector field ψ~T is a conformal vector field.