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| 摘要: |
| 在本论文中,我们研究了完备叶状黎曼流形上的基本p-调和形式.利用文献[1]中的方法,我们得到了在基本平均曲率形式满足有界且余闭的,以及横截曲率算子满足非负其至少在一点是正的假设下完备叶状黎曼流形上Lp-可积p-调和r-形式的一个消灭定理. |
| 关键词: 基本p-调和形式 消灭定理 叶状黎曼流形 |
| DOI： |
| 分类号:O186.15 |
| 基金项目:supported by Guangzhou Science and Technology Program(202102021174); Guangdong Basic and Applied Basic Research Foundation(2023A1515012121); supported by the Natural Science Foundation of Jiangsu Province (BK20230900); the Fundamental Research Funds for the Central Universities (30924010838); supported by NSF in China(12141104). |
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| VANISHING THEOREMS OF THE BASIC P-HARMONIC FORMS ON COMPLETE FOLIATED RIEMANNIAN MANIFOLDS |
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NIE Yan-ci,SHEN Zheng-han
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| Abstract: |
| In this paper, we study the basic p-harmonic forms on the complete foliated Riemannian manifolds. By using the method in [1], we show that if the basic mean curvature form is bounded and co-closed, and the transversal curvature operator is nonnegative and positive at least one point, then we obtain a vanishing theorem for Lp-integrably p-harmonic r-forms. |
| Key words: basic p-harmonic form vanishing theorem foliated Riemannian manifold |
