The Einstein-harmonic equations and constant scalar curvature Kähler metrics

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2024-06-12 DOI:10.1016/j.geomphys.2024.105253

Hajime Ono

引用次数: 0

Abstract

Let $(M, J)$ be a compact complex surface. In his paper [9], LeBrun showed that J-invariant solutions of the Einstein-Maxwell equations correspond to conformally Kähler constant scalar curvature metrics whose Ricci tensors are J-invariant. In the present paper, we prove that constant scalar curvature Kähler manifolds of even complex dimension give solutions of Einstein equations with matter fields which we call the Einstein-harmonic equations.

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爱因斯坦谐波方程和恒定标量曲率凯勒度量

让 (M,J) 是一个紧凑的复曲面。勒布伦在他的论文[9]中指出，爱因斯坦-麦克斯韦方程的 J 不变解对应于保角 Kähler 恒标量曲率流形，其 Ricci 张量是 J 不变的。在本文中，我们将证明偶复维度的凯勒恒定标量曲率流形给出了有物质场的爱因斯坦方程的解，我们称之为爱因斯坦-谐波方程。

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

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