Hadamard流形的子流形上的一些p-调和形式的消灭定理  

SOME VANISHING THEOREMS FOR p-HARMONIC FORMS ON SUBMANIFOLDS IN HADAMARD MANIFOLDS

作　　者：李南 沈正晗 LI Nan;SHEN Zheng-han(School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学数学与统计学院,江苏南京210094

出　　处：《数学杂志》2024年第4期293-308,共16页Journal of Mathematics

基　　金：Supported by the National Key R and D Program of China(2020YFA0713100);the Natural Science Foundation of Jiangsu Province(BK20230900);National Natural Science Foundation of China(12141104)。

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/p^(2)),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-k^(2)≤K_(N)≤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.In this paper,we give some vanishing theorems for p-harmonic forms on a comm-plete submanifold M immersed in Hadamard manifold N.Firstly,assume that M satisfies the weighted Poincar´e inequality and hasflat 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/p^(2))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-k^(2)≤K_(N)≤0 for some constant k.If the total curvature is small enough and thefirst 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].

关 键 词：p-调和形式 消灭定理 加权庞加莱不等式 Hadamard流形 

分 类 号：O186.15[理学—数学]