On the geometry of compatible Poisson and Riemannian structures

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-07-16 DOI:10.1016/j.geomphys.2025.105593

Nicolás Martínez Alba , Andrés Vargas

引用次数: 0

Abstract

We consider compatibility conditions between Poisson and Riemannian structures on smooth manifolds by means of a contravariant Levi-Civita connection. These include Riemann–Poisson structures (as defined by M. Boucetta), and the class of almost Kähler–Poisson manifolds, introduced with the aid of a contravariant f-structure, that will be called partially co-complex structure, in analogy with complex ones on Kähler manifolds. Additionally, we study the geometry of the symplectic foliation, and the behavior of these compatibilities under structure preserving maps and symmetries.

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相容泊松和黎曼结构的几何

利用逆变列维-奇维塔连接研究光滑流形上泊松结构和黎曼结构的相容条件。这些包括黎曼-泊松结构（由M. Boucetta定义），以及一类几乎Kähler-Poisson流形，借助逆变f结构引入，称为部分共复结构，类似于Kähler流形上的复结构。此外，我们还研究了辛叶理的几何性质，以及这些相容在保结构映射和对称下的行为。

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