The Global Pinching Theorem About Minimal Curvature Submanifolds

The curvature submanifold is a natural generalization of the concept of curvature line in classical surface theory.It is not only a kind of natural submanifold geometry,but also plays a very important role in the study of the Lie sphere geometry.The purpose of this paper is to study the minimal curvature submanifold of hy-persurfaces in the Euclidean space.The so-called minimal curvature submanifold,that is,the submanifold itself is both a curvature submanifold and a minimal submanifold.This article mainly uses the basic equation of the general Riemannian submanifold under the moving frame method,deduced the Gauss equation,Codazzi equation and Ricci equation of the curvature submanifold.By using the basic equation of the cur-vature submanifold,we obtain the global Pinching theorem of the minimal curvature submanifolds.