Hadamard流形的子流形上的一些p-调和形式的消灭定理OACSTPCD
SOME VANISHING THEOREMS FOR p-HARMONIC FORMS ON SUBMANIFOLDS IN HADAMARD MANIFOLDS
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;-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.
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 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].
李南;沈正晗
南京理工大学数学与统计学院,江苏南京 210094
数学
p-调和形式消灭定理加权庞加莱不等式Hadamard流形
p-harmonic formsvanishing theoremsweighted Poincaré inequalityHadamard manifolds
《数学杂志》 2024 (004)
293-308 / 16
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).
评论