双胞胎在Kähler和佐佐木几何

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-07-09 DOI:10.1016/j.geomphys.2025.105591

Charles P. Boyer , Hongnian Huang , Eveline Legendre , Christina W. Tønnesen-Friedman

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引用次数: 0

摘要

我们引入了加权极值Kähler双胞胎的概念以及相关的极值Sasaki双胞胎的概念。在Kähler设置中，这导致孪生现象出现在第一个Hirzebruch曲面[36]上的爱因斯坦-麦克斯韦方程组的LeBrun强厄米解到一般Hirzebruch曲面上的加权极值度量之间的推广。我们发现出现了许多双胞胎，这可以在佐佐木的设置中被视为在佐佐木锥中有多个极端射线的情况，即使我们不允许在同位素类中进行更改。我们也研究极端佐佐木双胞胎直接在佐佐木设置，主要集中在环佐佐木的情况下。

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Twins in Kähler and Sasaki geometry

We introduce the notions of weighted extremal Kähler twins together with the related notion of extremal Sasaki twins. In the Kähler setting this leads to a generalization of the twinning phenomenon appearing among LeBrun's strongly Hermitian solutions to the Einstein-Maxwell equations on the first Hirzebruch surface [36] to weighted extremal metrics on Hirzebruch surfaces in general. We discover that many twins appear and that this can be viewed in the Sasaki setting as a case where we have more than one extremal ray in the Sasaki cone even when we do not allow changes within the isotopy class. We also study extremal Sasaki twins directly in the Sasaki setting with a main focus on the toric Sasaki case.

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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