欧氏空间中紧致子流形的积分公式  

INTEGRAL FORMULAS FOR COMPACT SUBMANIFOLDS IN EUCLID SPACE

作　　者：王琪[1] 周志进[1] WANG Qi;ZHOU Zhi-jin(School of Mathematics and Information Science,Guiyang University,Guiyang 550005,China)

机构地区：[1]贵阳学院数学与信息科学学院,贵州贵阳550005

出　　处：《数学杂志》2020年第4期415-420,共6页Journal of Mathematics

基　　金：Supported by the Special Funding of Guiyang Science and Technology Bureau and Guiyang University(GYU-KYZ[2019-2020]).

摘　　要：本文研究了(n+p)维欧氏空间Rn+p中n维定向紧致无边子流形Mn的积分公式的问题.首先定义了Mn沿其单位平均曲率向量场ξ方向的高阶平均曲率Hr(0≤r≤n);然后,利用活动标架与外微分法,获得了关于Mn的一个新的积分公式.新公式推广了余维数p=1即超曲面情况下的经典积分公式.In this paper,we study the problem of integral formulas for an oriented and compact n-dimension isometric immersion submanifold Mn without boundary in the(n+p)-dimension euclid space Rn+p.At first,we define the r-th higher order mean curvature Hr(0≤r≤n)along the direction of the unit mean curvature vector fieldξto Mn,and then we attain a new integral formula,by applying the method of moving frame and exterior differential,which generalizes a classical integral formula in the case of codimension p=1,that is in the case of hypersurfaces.

关 键 词：欧氏空间 紧致无边子流形 平均曲率向量场 高阶平均曲率 积分公式 

分 类 号：O186.16[理学—数学]