加权 p 基本谐波形式及其应用

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2024-06-06 DOI:10.1016/j.geomphys.2024.105241

Seoung Dal Jung , Jinhua Qian , Xueshan Fu

引用次数: 0

摘要

本文研究了加权黎曼曲面（M,g,F,e-fν）上对于某个基本函数 f 的加权 p 基本谐波形式。同时，我们证明了在某些广义加权曲率假设下不存在非难 Lfp 加权 p 基本谐波形式。最后，我们考虑了 (M,g,F,e-fν) 与 (M′,g′,F′)之间 (F,F′)(p,f) 谐波映射的柳维尔类型定理的应用。

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Weighted p-basic harmonic forms and its applications

In this paper, we study the weighted p-basic harmonic forms on a weighted Riemannian foliation $(M, g, F, e^{- f} ν)$ for some basic function f. At the same time, we prove that there is no non-trivial $L_{f}^{p}$ -weighted p-basic harmonic form under some assumptions about the generalized weighted curvature. Finally, we consider the Liouville type theorem for ${(F, F^{'})}_{(p, f)}$ -harmonic map between $(M, g, F, e^{- f} ν)$ and $(M^{'}, g^{'}, F^{'})$ as applications.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity

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