Compact gradient shrinking ρ-Einstein solitons with pinching conditions

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-04-30 DOI:10.1016/j.geomphys.2024.105216

Xiaomin Chen

引用次数: 0

Abstract

We prove that an n-dimensional, $n \geq 4$ , compact gradient shrinking ρ-Einstein soliton satisfying suitable pinching conditions and curvature conditions is isometric to a quotient of the round sphere $S^{n}$ . Our results extend the rigidity theorems given by Huang (Integral pinched gradient shrinking ρ-Einstein solitons, 2017) in dimension $4 \leq n \leq 6$ .

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具有捏合条件的紧凑梯度收缩ρ-爱因斯坦孤子

我们证明，满足合适捏合条件和曲率条件的n维、n≥4、紧凑梯度收缩ρ-爱因斯坦孤子与圆球Sn的商等距。我们的结果扩展了 Huang（Integral pinched gradient shrinking ρ-Einstein solitons, 2017）给出的 4≤n≤6 维的刚性定理。

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