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| 摘要: |
| 本文研究了Hadamard流形N的完备浸入子流形M上的一些p-调和形式的消灭定理.首先, 假设M满足加权庞加莱不等式且具有平坦法丛,N具有纯曲率张量且(l,n-l)-曲率不小于-kρ (0≤k≤4/p2),2≤l≤n-2. 如果总曲率足够小, 我们得到了p-调和l-形式的消灭定理,推广了Wang-Chao-Wu-Lv在2018年的结果. 其次, 假设N是一个截面曲率满足-k2≤KN≤ 0的Hadamard流形,如果总曲率足够小且拉普拉斯的第一特征值满足某个下界,我们得到了p-调和1-形式的消灭定理, 推广了Dung-Seo在2015年的结果. |
| 关键词: p-调和形式 消灭定理 加权庞加莱不等式 Hadamard流形 |
| DOI： |
| 分类号:O186.15 |
| 基金项目: |
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| SOME VANISHING THEOREMS FOR p-HARMONIC FORMS ON SUBMANIFOLDS IN HADAMARD MANIFOLDS |
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LI Nan,SHEN Zheng-han
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| Abstract: |
| In this paper, we give some vanishing theorems for p-harmonic forms on a commplete submanifold M immersed in Hadamard manifold N. Firstly, assume that M satisfies the weighted Poincaré inequality and has flat normal bundle. And assume further that N has pure curvature tensor and the (l,n-l)-curvature of N is not less than kρ (0≤k≤4/p2) for 2≤l≤n-2. If the total curvature is small enough, we prove a vanishing theorem for p-harmonic $l$-forms, which generalizes Wang-Chao-Wu-Lv's results in [1]. Secondly, suppose that N is a Hadamard manifold with sectional curvature -k2≤KN≤ 0 for some constant k. If the total curvature is small enough and the first eigenvalue of Laplace satisfies a certain lower bound, we obtain a vanishing theorem for p-harmonic 1-forms, which generalizes Dung-Seo's results in [2]. |
| Key words: p-harmonic forms vanishing theorems weighted Poincaré inequality Hadamard manifolds |
