翘积流形上的梯度 h˜-almost 里奇孤子

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-09-20 DOI:10.1016/j.geomphys.2024.105325

Dong Shen, Jiancheng Liu

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引用次数: 0

摘要

在本文中，我们利用强最大原则，提出了构造具有翘曲积结构的梯度 h˜-几乎 Ricci 孤子的必要条件和充分条件，并给出了由我们的构造产生的 PDE 的特定解的例子。此外，我们还证明了在关于翘曲函数或梯度向量场的一些自然假设下，翘曲积流形上梯度 h˜-almost Ricci 孤子的非存在性结果。

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Gradient h˜-almost Ricci solitons on warped product manifolds

In this paper, by using the strong maximum principle, we present a necessary and sufficient conditions for constructing gradient

\tilde{h}

-almost Ricci solitons with warped product structures, and give examples of particular solutions of the PDEs that arise from our construction. Also, we prove nonexistence results for gradient

\tilde{h}

-almost Ricci solitons on warped product manifolds under some natural assumptions concerning the warping function or gradient vector field.

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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