Differential Geometry and its Applications最新文献

英文中文

Rigidity of closed minimal hypersurfaces in S5 S5中闭极小超曲面的刚性

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-09-01 Epub Date: 2025-05-09 DOI: 10.1016/j.difgeo.2025.102252

Pengpeng Cheng, Tongzhu Li

Let

M^{4} \to S^{5}

be a closed immersed minimal hypersurface with constant squared length of the second fundamental form S in a 5-dimensional sphere

S^{5}

. In this paper, we prove that if the 3-mean curvature

H_{3}

and the number g of the distinct principal curvatures are constant, then

M^{4}

is an isoparametric hypersurface, and the value of S can only be

0, 4, 12

. This result supports Chern Conjecture.

设M4→S5为5维球面S5中第二基本形式S的平方长度为常数的封闭浸没极小超曲面。在本文中，我们证明了如果3-平均曲率H3和不同主曲率的个数g是常数，则M4是一个等参超曲面，且S的值只能为0,4,12。这一结果支持陈猜想。

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 : 2025-09-01 Epub 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

Orlicz harmonic version of dual mixed volumes 奥尔利茨调和版的双混合卷

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-09-01 Epub Date: 2025-07-02 DOI: 10.1016/j.difgeo.2025.102268

Chang-Jian Zhao

In the paper, our main aim is to generalize the dual mixed harmonic quermassintegrals to Orlicz space. Under the framework of Orlicz dual Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating Orlicz first order variation of the dual mixed harmonic quermassintegrals, and call it the Orlicz dual mixed harmonic quermassintegrals. The fundamental notions and conclusions of the dual mixed harmonic quermassintegrals and the Minkowski and Brunn-Minkowski inequalities for the dual harmonic quermassintegrals are extended to an Orlicz setting, and the related concepts and inequalities of Orlicz dual mixed volumes are also included in our conclusions.

本文的主要目的是将对偶混合调和quermass积分推广到Orlicz空间。在Orlicz对偶Brunn-Minkowski理论的框架下，通过计算对偶混合调和quermass积分的Orlicz一阶变分，引入了一个新的仿射几何量，称为Orlicz对偶混合调和quermass积分。将对偶混合调和quermass积分的基本概念和结论以及对偶调和quermass积分的Minkowski不等式和Brunn-Minkowski不等式推广到一个Orlicz集合中，并将Orlicz对偶混合体积的相关概念和不等式也包含在我们的结论中。

引用次数: 0

Higher-power harmonic maps, instantons and Yang-Mills theory 高功率谐波映射，瞬子和杨-米尔斯理论

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-06-01 Epub Date: 2025-03-09 DOI: 10.1016/j.difgeo.2025.102240

Elias Knack, Henrik Naujoks

Let

(M, g)

and

(N, h)

be two pseudo-Riemannian manifolds. We study field theoretic properties of higher-power harmonic maps (also called r-harmonic maps)

φ : M \to N

, which are a natural generalization of standard harmonic maps first introduced by C. Wood. In particular, we discuss the coupled system of higher-power harmonic maps and the Einstein-Hilbert action and prove a sufficient condition for a map to be r-harmonic, which is highly motivated by classical field equations like the harmonic map equation or the Yang-Mills equation. Furthermore, we derive an instanton theory for r-harmonic maps on 2r-dimensional base manifolds and investigate conformal properties of general higher-power harmonic maps. Finally, since the theory of higher-power harmonic maps bears striking similarities with Yang-Mills theory, we provide a comprehensive comparison between the two theories which explains in more detail surprisingly many analogies.

设（M,g）和（N,h）是两个伪黎曼流形。本文研究了高次谐波映射φ:M→N的场论性质，这是C. Wood首次提出的标准谐波映射的自然推广。特别地，我们讨论了高次谐波映射的耦合系统和Einstein-Hilbert作用，并证明了一个映射是r-调和的充分条件，这是由调和映射方程或Yang-Mills方程等经典场方程高度激励的。在此基础上，导出了二维基流形上r调和映射的瞬子理论，并研究了一般高次调和映射的共形性质。最后，由于高功率谐波映射理论与杨-米尔斯理论有着惊人的相似之处，我们对这两种理论进行了全面的比较，更详细地解释了令人惊讶的许多相似之处。

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引用次数: 0

Regulated curves on a Banach manifold and singularities of endpoint map. I. Banach manifold structure Banach流形上的调节曲线及端点映射的奇异性。1 .巴拿赫流形结构

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-06-01 Epub Date: 2025-03-27 DOI: 10.1016/j.difgeo.2025.102245

Tomasz Goliński , Fernand Pelletier

We consider regulated curves in a Banach bundle whose projection on the basis is continuous with regulated derivative. We build a Banach manifold structure on the set of such curves. This result was previously obtained for the case of strong Riemannian Banach manifold and absolutely continuous curves in [16]. The essential argument used was the existence of a “local addition” on such a manifold. Our proof is true for any Banach manifold. In the second part of the paper the problems of controllability will be discussed.

考虑Banach束上的可调曲线，其在基上的投影是连续的，导数是可调的。我们在这些曲线的集合上建立了一个Banach流形结构。这一结果已在强黎曼巴拿赫流形和[16]中绝对连续曲线的情况下得到。所用的基本论证是在这种流形上存在一个“局部加法”。我们的证明对任何巴拿赫流形都成立。论文的第二部分将讨论可控性问题。

引用次数: 0

On the integration of Manin pairs 关于Manin对的积分

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-06-01 Epub Date: 2025-04-04 DOI: 10.1016/j.difgeo.2025.102246

David Li-Bland, Eckhard Meinrenken

It is a remarkable fact that the integrability of a Poisson manifold to a symplectic groupoid depends only on the integrability of its cotangent Lie algebroid A: The source-simply connected Lie groupoid

G ⇉ M

integrating A automatically acquires a multiplicative symplectic 2-form. More generally, a similar result holds for the integration of Lie bialgebroids to Poisson groupoids, as well as in the ‘quasi’ settings of Dirac structures and quasi-Lie bialgebroids. In this article, we will place these results into a general context of Manin pairs

(E, A)

, thereby obtaining a simple geometric approach to these integration results. We also clarify the case where the groupoid G integrating A is not source-simply connected. Furthermore, we obtain a description of Hamiltonian spaces for Poisson groupoids and quasi-symplectic groupoids within this formalism.

泊松流形对辛群似体的可积性仅取决于其余切李代数似体a的可积性，这是一个值得注意的事实：对a积分的源单连通李群似体G M自动获得了一个乘法辛2型。更一般地说，对于李双代数群与泊松群的积分，以及在狄拉克结构和拟李双代数群的“拟”设置中，也有类似的结果。在本文中，我们将把这些结果放在Manin对（E, a）的一般上下文中，从而获得这些积分结果的简单几何方法。我们还澄清了对A积分的群形G不是源单连通的情况。在此基础上，得到了泊松群和拟辛群的哈密顿空间的描述。

引用次数: 0

Ramification and unicity theorems for Gauss maps of complete space-like stationary surfaces in four-dimensional Lorentz-Minkowski space 四维洛伦兹-闵可夫斯基空间中完全类空固定曲面高斯映射的分支和唯一性定理

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-06-01 Epub Date: 2025-02-27 DOI: 10.1016/j.difgeo.2025.102238

Li Ou

In this paper, we investigate value distribution properties for Gauss maps of space-like stationary surfaces in four-dimensional Lorentz-Minkowski space

R^{3, 1}

, focusing on aspects such as the total weight of totally ramified values and unicity properties. We obtain not only general conclusions analogous to those in four-dimensional Euclidean space, but also results for space-like stationary surfaces with rational graphical Gauss image, which is an extension of degenerate space-like stationary surfaces.

本文研究了四维洛伦兹-闵可夫斯基空间R3,1中类空固定曲面的高斯映射的值分布性质，重点研究了全分支值的总权重和唯一性性质。我们不仅得到了类似于四维欧几里得空间的一般结论，而且还得到了具有理性图形高斯像的类空间静止曲面的结果，它是退化类空间静止曲面的扩展。

引用次数: 0

The strong Diederich-Fornæss index on C2 domains in Hermitian manifolds 厄米流形中C2域上的强Diederich-Fornæss指标

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-06-01 Epub Date: 2025-04-24 DOI: 10.1016/j.difgeo.2025.102251

Phillip S. Harrington

For a relatively compact Stein domain Ω with

C^{2}

boundary in a Hermitian manifold M, we consider the strong Diederich-Fornæss index, denoted

D F (Ω)

: the supremum of all exponents

0 < η < 1

such that eigenvalues of the complex Hessian of

- {(- ρ)}^{η}

are bounded below by some positive multiple of

{(- ρ)}^{η}

on Ω for some

C^{2}

defining function ρ. We will show that

D F (Ω)

is completely characterized by the existence of a Hermitian metric with curvature terms satisfying a certain inequality when restricted to the null-space of the Levi-form.

对于厄米流形M中具有C2边界的相对紧凑的Stein定域Ω，我们考虑强diederlich - forn æss指标，记为DF（Ω）：所有指数0<；η<；1的极值，使得-(−ρ)η的复Hessian的特征值在Ω上被某个C2定义函数ρ的正倍数有界。我们将证明DF（Ω）是完全由曲率项满足一定不等式的厄米度规的存在所表征的，当它被限制在列维形式的零空间中时。

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引用次数: 0

Curvature pinching for three-dimensional submanifolds in a Riemannian manifold 黎曼流形中三维子流形的曲率缩紧

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-06-01 Epub Date: 2025-02-05 DOI: 10.1016/j.difgeo.2025.102234

Juanru Gu , Yao Lu , Hongwei Xu , Entao Zhao

Let

M^{3}

be an oriented submanifold with parallel mean curvature vector in a complete simply connected Riemannian manifold

N^{3 + p}

. When the mean curvature

H = 0

, i.e., M is minimal, we prove that there exists a constant

δ_{1} (p) \in (0, 1)

, such that if

{\overline{K}}_{N} \in [δ_{1} (p), 1]

, and if M has a lower bound for Ricci curvature and an upper bound for scalar curvature, then

N^{3 + p}

is isometric to

S^{3 + p}

. Moreover, M is the totally geodesic sphere

S^{3}

. This is a generalization of Shen and Li's results [10], [14]. When the ambient manifold is a space form, we improve the geometric rigidity theorem due to Xu-Gu [19] for the codimension is not more than 2 and

H \neq 0

设M3为完全单连通黎曼流形N3+p中具有平行平均曲率矢量的有向子流形。当平均曲率H=0，即M最小时，我们证明存在一个常数δ1(p)∈(0,1)，使得如果K - N∈[δ1(p),1]，并且M有里奇曲率的下界和标量曲率的上界，那么N3+p与S3+p是等距的。M为全测地线球S3。这是Shen和Li的结果b[10] b[14]的推广。当环境多方面的空间形式,我们提高刚性几何定理由于Xu-Gu[19]的余维数不超过2和H≠0。

引用次数: 0

Connection blocking in quotients of Sol Sol商中的连接阻塞

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications

Pub Date : 2025-06-01 Epub Date: 2025-03-09 DOI: 10.1016/j.difgeo.2025.102241

Reza Bidar

Let G be a connected Lie group and

Γ \subset G

a lattice. Connection curves of the homogeneous space

M = G / Γ

are the orbits of one parameter subgroups of G. To block a pair of points

m_{1}, m_{2} \in M

is to find a finite set

B \subset M ∖ {m_{1}, m_{2}}

such that every connecting curve joining

m_{1}

and

m_{2}

intersects B. The homogeneous space M is blockable if every pair of points in M can be blocked, otherwise we call it non-blockable.

Sol is an important Lie group and one of the eight homogeneous Thurston 3-geometries. It is a unimodular solvable Lie group diffeomorphic to

R^{3}

, and together with the left invariant metric

d s^{2} = e^{- 2 z} d x^{2} + e^{2 z} d y^{2} + d z^{2}

includes copies of the hyperbolic plane, which makes studying its geometrical properties more interesting. In this paper we prove that all lattice quotients of Sol are non-blockable. In particular, we show that for any lattice

Γ \subset S o l

, the set of non-blockable pairs is a dense subset of

S o l / Γ \times S o l / Γ

设G是连通李群，Γ∧G是晶格。齐次空间M=G/Γ的连接曲线是G的一个参数子群的轨道。要阻塞一对点m1，m2∈M，就是找到一个有限集合B∧M∈{m1，m2}使得连接m1和m2的每条连接曲线都与B相交，则齐次空间M是可阻塞的，如果M中的每对点都能被阻塞，则称之为不可阻塞。Sol是一个重要的李群，是8个齐次Thurston 3几何之一。它是微分同构于R3的单模可解李群，与左不变度规ds2=e−2zdx2+e2zdy2+dz2一起包含了双曲平面的副本，这使得研究其几何性质变得更加有趣。本文证明了Sol的所有格商都是不可阻塞的。特别地，我们证明了对于任意晶格Γ∧Sol，不可阻塞对的集合是Sol/Γ×Sol/Γ的密集子集。

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引用次数: 0

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Differential Geometry and its Applications

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