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| 关于极小曲面度量特征的一个证明 | |
| 引用本文： | 王焱平,张伟,郭新伟.关于极小曲面度量特征的一个证明[J].南昌大学学报(理科版),2009,33(3). |
| 作者姓名： | 王焱平 张伟 郭新伟 |
| 作者单位： | 1. 上海电力学院,数理系,上海,200090 2. 北京大学,数学科学学院,北京,100871 3. 山东大学,威海分校数学系,山东,威海,264209 |
| 基金项目： | 上海市科学技术委员会资助项目 |
| 摘 要： | 通过构造某个乘积流形中的一个子流形Q及Q上外微分式环中某个理想的一组生成元,利用4]的主要工作,在这里证明了理想是d-封闭的.从而确定了一个3维积分子流形S .并由此给出了空间形式中一类极小曲面的度量特征的一个独特的构造性的证明.其中关于丛映射的证明对一般情形也适用,从而弥补了3]中该部分的缺陷. |
| 关 键 词： | 极小浸入 主丛 黎曼联络 Frobenius定理 积分子流形 |
A Proof For the Metric Characterization of a Class of Minimal Surfaces |
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| WANG Yan-ping,ZHANG Wei,GUO Xin-wei.A Proof For the Metric Characterization of a Class of Minimal Surfaces[J].Journal of Nanchang University(Natural Science),2009,33(3). | |
| Authors: | WANG Yan-ping ZHANG Wei GUO Xin-wei |
| Affiliation: | 1.Department of Mathematics and Physics;Shanghai University of Electric Power;Shanghai 200090;China;2.School of Mathematical Sciences;Peking University;Beijing 100871;3.Department of Mathematics Shandong University Weihai;Shandong Weihai 264209;China |
| Abstract: | By constructing a submanifold Q of some product manifold and a set of ideal generators for some ideal in the ring of exterior differential forms on Q;and by making use of the main works in 4],we proved that the ideal is d-closed.Thus it determines a 3-dimensional integral submanifold S,and thereout we give a unique and constructive proof for the metric characterizations of a sort of minimal surfaces in space forms,therein the proof for the bundle maps also applies to general case,and it also makes up the d... |
| Keywords: | minimal immersion principal bundle Riemannian connection Frobenius theorem integral submanifold |
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