Differential Geometry and its Applications最新文献

英文中文

Stochastic Euler-Poincaré reduction for central extension 中心扩展的随机euler - poincarcarr约简

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-09-11 DOI: 10.1016/j.difgeo.2025.102290

Ali Suri

This paper explores the application of central extensions of Lie groups and Lie algebras to derive the viscous quasi-geostrophic (QGS) equations, with and without Rayleigh friction term, on the torus as critical points of a stochastic Lagrangian. We begin by introducing central extensions and proving the integrability of the Roger Lie algebra cocycle

ω_{α}

, which is used to model the QGS on the torus. Incorporating stochastic perturbations, we formulate two specific semi-martingales on the central extension and study the stochastic Euler-Poincaré reduction. Specifically, we add stochastic perturbations to the

g

part of the extended Lie algebra

\hat{g} = g ⋊_{ω_{α}} R

and prove that the resulting critical points of the stochastic right-invariant Lagrangian solve the viscous QGS equation, with and without Rayleigh friction term.

利用李群和李代数的中心扩展，导出了作为随机拉格朗日点的环面上具有和不具有瑞利摩擦项的粘性拟地转方程。我们首先引入中心扩展并证明了罗杰李代数环ωα的可积性，该环ωα用于环面上QGS的建模。考虑随机扰动，我们在中心扩展上构造了两个特定的半鞅，并研究了随机euler - poincarcarr约化。具体地说，我们在扩展李代数g =g ωαR的g部分加入随机扰动，并证明了得到的随机右不变拉格朗日的临界点可以解有或没有瑞利摩擦项的粘性QGS方程。

引用次数: 0

Minimal and harmonic vector fields on three-dimensional C12-manifolds 三维c12流形上的极小和调和向量场

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-09-11 DOI: 10.1016/j.difgeo.2025.102289

Gherici Beldjilali

In this paper, we obtain some necessary and sufficient conditions for a vector field on a 3-dimensional

C_{12}

-manifold to be minimal or harmonic. We construct some examples to illustrate main results.

本文给出了三维c12流形上向量场最小或调和的几个充要条件。我们构造了一些例子来说明主要结果。

引用次数: 0

The completeness problem on the pseudo-homothetic Lie group 伪齐调李群上的完备性问题

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-09-09 DOI: 10.1016/j.difgeo.2025.102288

Salah Chaib , Ana Cristina Ferreira , Abdelghani Zeghib

Let us call pseudo-homothetic group the non-unimodular 3-dimensional Lie group that is the semi-direct product of

R

acting non-semisimply on

R^{2}

. In this article, we solve the geodesic completeness problem on this Lie group. In particular, we exhibit a family of complete metrics such that all geodesics have bounded velocity. As an application, we show that the set of complete metrics is not closed.

我们称伪同群为非单模的三维李群，它是R作用于R2上的非半单模的半直积。本文解决了该李群上的测地线完备性问题。特别地，我们展示了一组完备的度量，使得所有测地线的速度都有界。作为一个应用程序，我们展示了完整度量的集合不是封闭的。

引用次数: 0

Minimal hypersurfaces in S5 with constant scalar curvature and zero Gauss curvature 具有常标量曲率和零高斯曲率的S5极小超曲面

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-09-09 DOI: 10.1016/j.difgeo.2025.102279

Qing Cui

We show that a closed minimal hypersurface in

S^{5}

with constant scalar curvature and zero Gauss curvature is totally geodesic, which gives a support to strong version of Chern conjecture.

我们证明了S5中具有恒定标量曲率和零高斯曲率的闭极小超曲面是完全测地线的，这为强版本的陈氏猜想提供了支持。

引用次数: 0

Stability and rigidity of 3-Lie algebra morphisms 3-Lie代数态射的稳定性和刚性

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-09-02 DOI: 10.1016/j.difgeo.2025.102278

Jun Jiang, Yunhe Sheng, Geyi Sun

In this paper, first we use the higher derived brackets to construct an

L_{\infty}

-algebra, whose Maurer-Cartan elements are 3-Lie algebra morphisms. Using the differential in the

L_{\infty}

-algebra that govern deformations of the morphism, we give the cohomology of a 3-Lie algebra morphism. Then we study the rigidity and stability of 3-Lie algebra morphisms using the established cohomology theory. In particular, we show that if the first cohomology group is trivial, then the morphism is rigid; if the second cohomology group is trivial, then the morphism is stable. Finally, we study the stability of 3-Lie subalgebras similarly.

本文首先利用高导括号构造了一个L∞代数，其Maurer-Cartan元是3-Lie代数的态射。利用控制态射变形的L∞代数中的微分，给出了3-李代数态射的上同调。然后利用已建立的上同调理论研究了3-李代数态射的刚性和稳定性。特别地，我们证明了如果第一个上同群是平凡的，则态射是刚性的；如果第二个上同群是平凡的，则模射是稳定的。最后，我们同样研究了3-Lie子代数的稳定性。

引用次数: 0

Hamilton Lie algebroids over Dirac structures and sigma models 狄拉克结构和模型上的汉密尔顿李代数

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-08-25 DOI: 10.1016/j.difgeo.2025.102277

Noriaki Ikeda

We propose a Hamiltonian Lie algebroid and a momentum section over a Dirac structure as a generalization of a Hamiltonian Lie algebroid over a pre-symplectic manifold and one over a Poisson manifold. A Hamiltonian Lie algebroid and a momentum section generalize a Hamiltonian G-space and a momentum map over a symplectic manifold. We prove some properties of this new Hamiltonian Lie algebroid and construct a mechanics based on this structure as an application. These new mechanics are called the gauged Poisson sigma model and the gauged Dirac sigma model.

作为前辛流形和泊松流形上的哈密顿李代数体的推广，我们提出了一个哈密顿李代数体和狄拉克结构上的动量截面。一个哈密顿李代数体和一个动量截面推广了一个哈密顿g空间和一个辛流形上的动量映射。我们证明了这个新哈密顿李代数的一些性质，并以此为应用构造了一个力学。这些新的力学被称为量规泊松模型和量规狄拉克模型。

引用次数: 0

On the structure of homogeneous local Poisson brackets 齐次局部泊松括号的结构

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-08-25 DOI: 10.1016/j.difgeo.2025.102276

Guido Carlet , Matteo Casati

We consider an arbitrary Dubrovin-Novikov bracket of degree k, namely a homogeneous degree k local Poisson bracket on the loop space of a smooth manifold M of dimension n, and show that k connections, defined by explicit linear combinations with constant coefficients of the standard connections associated with the Poisson bracket, are flat.

我们考虑一个k度的任意Dubrovin-Novikov括号，即n维光滑流形M的环空间上的一个k次齐次局部泊松括号，并证明由泊松括号相关的标准连接的常系数显式线性组合所定义的k个连接是平坦的。

引用次数: 0

A Simons type condition for instability of F-Yang-Mills connections F-Yang-Mills连接不稳定的Simons型条件

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-08-20 DOI: 10.1016/j.difgeo.2025.102275

Kurando Baba , Kazuto Shintani

F-Yang-Mills connections are critical points of F-Yang Mills functional on the space of connections of a principal fiber bundle, which are generalizations of Yang-Mills connections, p-Yang-Mills connections and exponential Yang-Mills connections and so on. Here, F is a strictly increasing

C^{2}

-function. In this paper, we extend Simons theorem for the instability of Yang-Mills connections to F-Yang-Mills connections. We derive a sufficient condition that any non-flat, F-Yang-Mills connection over submanifolds in a Euclidean space is unstable. In the standard sphere case, this condition is expressed by an inequality involving its dimension and the degree of the differential of the function F. Our main results are proved by extending Kobayashi-Ohnita-Takeuchi's calculation to F-Yang-Mills connections.

F-Yang-Mills连接是在主纤维束连接空间上泛函的F-Yang Mills的临界点，它是Yang-Mills连接、p-Yang-Mills连接和指数Yang-Mills连接等的推广。这里，F是严格递增的c2函数。本文将Yang-Mills连接不稳定性的Simons定理推广到F-Yang-Mills连接。给出了欧几里德空间中子流形上的任何非平坦的F-Yang-Mills连接是不稳定的一个充分条件。在标准球面情况下，这个条件用一个涉及到它的维数和函数f的微分阶数的不等式来表示。我们的主要结果通过将Kobayashi-Ohnita-Takeuchi的计算推广到F-Yang-Mills连接得到证明。

引用次数: 0

Manin triples on multiplicative Courant algebroids 乘法Courant代数上的Manin三元组

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-08-01 DOI: 10.1016/j.difgeo.2025.102273

Ana Carolina Mançur

We extend the characterization of Lie bialgebroids via Manin triples to the context of double structures over Lie groupoids. We consider Lie bialgebroid groupoids, given by LA-groupoids in duality, and establish their correspondence with multiplicative Manin triples, i.e., CA-groupoids equipped with a pair of complementary multiplicative Dirac structures. As an application, we give a new viewpoint to the co-quadratic Lie algebroids of Lang, Qiao, and Yin [13] and the Manin triple description of Lie bialgebroid crossed modules.

我们通过Manin三元组将李双代数群的表征推广到李群上的双结构。我们考虑由对偶性的la -群拟给出的李双代数群拟，并建立了它们与乘法Manin三元组的对应关系，即ca -群拟具有一对互补的乘法Dirac结构。作为应用，我们给出了Lang、Qiao、Yin的共二次李代数体和李双代数体交叉模的Manin三重描述的新观点。

引用次数: 0

Multisymplectic observable reduction using constraint triples 约束三元组的多辛可观察约简

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-07-16 DOI: 10.1016/j.difgeo.2025.102272

Antonio Michele Miti , Leonid Ryvkin

The purpose of this paper is to present a fully algebraic formalism for the construction and reduction of

L_{\infty}

-algebras of observables inspired by multisymplectic geometry, using Gerstenhaber algebras, BV-modules, and the constraint triple formalism. In the “geometric case”, we reconstruct and conceptually explain the recent results of [7].

本文的目的是利用Gerstenhaber代数、bv模和约束三重形式，给出由多辛几何启发的L∞-可观测代数的构造和约简的完全代数形式。在“几何情况”下，我们对[7]的最新结果进行了重构和概念解释。

引用次数: 0

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