Geometry of bundle-valued multisymplectic structures with Lie algebroids

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-06-07 DOI:10.1016/j.geomphys.2024.105242

Yuji Hirota , Noriaki Ikeda

引用次数: 0

Abstract

We study multisymplectic structures taking values in vector bundles with connections from the viewpoint of the Hamiltonian symmetry. We introduce the notion of bundle-valued n-plectic structures and exhibit some properties of them. In addition, we define bundle-valued homotopy momentum sections for bundle-valued n-plectic manifolds with Lie algebroids to discuss momentum map theories in both cases of quaternionic Kähler manifolds and hyper-Kähler manifolds. Furthermore, we generalize the Marsden-Weinstein-Meyer reduction theorem for symplectic manifolds and construct two kinds of reductions of vector-valued 1-plectic manifolds.

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带 Lie algebroids 的束值多折射结构几何学

我们从哈密顿对称性的角度研究在有连接的向量束中取值的多折射结构。我们引入了束值 n-折射结构的概念，并展示了它们的一些性质。此外，我们定义了具有Lie algebroids的束值n-折射流形的束值同调动量部分，以讨论四元凯勒流形和超凯勒流形两种情况下的动量映射理论。此外，我们还推广了交映流形的马斯登-韦恩斯坦-迈耶还原定理，并构建了两种向量值 1-折射流形的还原。

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