Variation formulas and Jiang's theorem for f-biharmonic maps on Riemannian foliations

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-07-30 DOI:10.1016/j.geomphys.2025.105604

Xueshan Fu , Jinhua Qian , Seoung Dal Jung

引用次数: 0

Abstract

On foliations, there are two kinds of harmonic maps, that is, transversally harmonic map and

(F, F^{'})

-harmonic map between Riemannian foliations

(M, g, F)

and

(M^{'}, g^{'}, F^{'})

. These are extended to another (bi)harmonic maps. In this paper, we study several harmonic and biharmonic maps on foliations. In particular, we give the variation formulas and prove the Jiang's theorem for transversally f-biharmonic map, transversally bi-f-harmonic map,

{(F, F^{'})}_{f}

-biharmonic map and bi-

{(F, F^{'})}_{f}

-harmonic maps on foliations, where f is a positive basic function.

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黎曼叶上f-双调和映射的变分公式和Jiang定理

在叶上有两种调和映射，即横向调和映射和（F,F ‘）——黎曼叶（M,g，F）和（M ’，g ',F '）之间的调和映射。这些被推广到另一个（双）调和映射。本文研究了叶上的调和映射和双调和映射。特别地，我们给出了叶上的横向F -双调和映射、横向双- F -调和映射、（F,F ‘） F -双调和映射和双-（F,F ’） F -调和映射的变分公式并证明了蒋定理，其中F是一个正基函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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