数学杂志2024，Vol.44Issue(4)：293-308,16.
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
摘要
Abstract
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].关键词
p-调和形式/消灭定理/加权庞加莱不等式/Hadamard流形Key words
p-harmonic forms/vanishing theorems/weighted Poincaré inequality/Hadamard manifolds分类
数理科学引用本文复制引用
李南,沈正晗..Hadamard流形的子流形上的一些p-调和形式的消灭定理[J].数学杂志,2024,44(4):293-308,16.基金项目
Supported by the National Key R and D Program of China(2020YFA0713100) （2020YFA0713100）
the Natural Science Foundation of Jiangsu Province(BK20230900) （BK20230900）
National Natural Science Foundation of China(12141104). （12141104）
