华东师范大学学报（自然科学版） >

2018 , Vol. 2018 >Issue 3: 38 - 45

DOI: https://doi.org/10.3969/j.issn.1000-5641.2018.03.005

数学

欧氏空间中超曲面的L2调和2-形式

  • 张全锐 ,
  • 刘建成
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  • 西北师范大学 数学与统计学院, 兰州 730070
张全锐,男,硕士研究生,研究方向为微分几何.E-mail:zhangqr90@163.com.

收稿日期: 2017-05-01

  网络出版日期: 2018-05-29

基金资助

国家自然科学基金（11261051，11761061）

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L2 harmonic 2-forms on a hypersurface in Euclidean space

  • ZHANG Quan-rui ,
  • LIU Jian-cheng
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  • College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received date: 2017-05-01

  Online published: 2018-05-29

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摘要

研究欧氏空间Rn+1（n≥3）中完备超曲面M上的L2调和2-形式.应用Bochner技巧，证明了当M的无迹对称张量Φ和平均曲率向量H的Ln（M）范数均有只依赖于n的适当上界时，M上的L2调和2-形式是平行的.进一步，若M为非极小超曲面，则M上不存在非平凡的L2调和2-形式.

关键词： 欧氏空间; 超曲面; L2调和2-形式; 非极小

本文引用格式

张全锐 , 刘建成 . 欧氏空间中超曲面的L2调和2-形式[J]. 华东师范大学学报（自然科学版）, 2018 , 2018(3) : 38 -45 . DOI: 10.3969/j.issn.1000-5641.2018.03.005

Abstract

In this paper, we study L2 harmonic 2-forms on a complete hypersurface M of Euclidean space Rn+1(n ≥ 3). By applying the Bochner technique, we prove that if the Ln(M) norms of the traceless second fundamental form Φ and the mean curvature vector H are both bounded from above by certain constants which depend only on n, then the L2 harmonic 2-forms on M are parallel. Furthermore, if M is a non-minimal hypersurface, then there is no nontrivial L2 harmonic 2-form on M.

Key words： Euclidean space; hypersurface; L2 harmonic 2-forms; non-minimal

参考文献

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