“具有全纯平凡正则束的六维齐次空间”的补充[J]。几何学。物理学报。194 (2023)105014]

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-06-20 DOI:10.1016/j.geomphys.2025.105570

Antonio Otal , Luis Ugarte

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引用次数: 0

摘要

在这篇文章中，我们重点讨论了在我们最近的论文“具有全纯平凡正则束的六维齐次空间”中缺失的一个可解李代数的复厄米几何。证明了它支持一个非零闭（3,0）形的唯一复结构，并描述了它的平衡厄米度量空间。证明了在由该李代数构造的溶剂流形上与任何不变平衡厄米度量相关的实例的不存在性。

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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Addendum to “Six dimensional homogeneous spaces with holomorphically trivial canonical bundle” [J. Geom. Phys. 194 (2023) 105014]

In this note we focus on the complex Hermitian geometry of a solvable Lie algebra that was missing in our recent paper “Six dimensional homogeneous spaces with holomorphically trivial canonical bundle”. We prove that it supports a unique complex structure with non-zero closed (3,0)-form, and we describe its space of balanced Hermitian metrics. The non-existence of instantons associated to any invariant balanced Hermitian metric on solvmanifolds constructed from that Lie algebra is also proved.

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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