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| 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. |
| 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 |
| DOI： |
| 分类号:O186.16 |
| 基金项目:Supported by the Special Funding of Guiyang Science and Technology Bureau and Guiyang University (GYU-KYZ[2019-2020]). |
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| INTEGRAL FORMULAS FOR COMPACT SUBMANIFOLDS IN EUCLID SPACE |
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WANG Qi,ZHOU Zhi-jin
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| Abstract: |
| 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 field ξ to 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. |
| Key words: euclid space compact submanifold without boundary mean curvature vector field higher order mean curvature integral formula |
