Journal of Geometry and Physics最新文献

{"title":"A characterization of a special planar 5-body central configuration with a trapezoidal convex hull","authors":"Yangshanshan Liu ,&nbsp;Shiqing Zhang","doi":"10.1016/j.geomphys.2025.105494","DOIUrl":"10.1016/j.geomphys.2025.105494","url":null,"abstract":"<div><div>We use mutual distances as coordinates to characterize a kind of central configuration of the planar Newtonian 5-body problem with a trapezoidal convex hull; namely, four of the five bodies are located at the vertices of a trapezoid, and the fifth one is located on one of the parallel sides. We demonstrate that if this central configuration exists, it is a unique local minimum of a particular Lagrangian function. Numerically, we show that this central configuration must be an isosceles trapezoid, and the parallel side containing three particles is shorter than the other one. In addition, the main result remains true when the fifth mass decreases to zero. We show at the end of this paper that the limiting case is a central configuration of the restricted (4+1)-body problem.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105494"},"PeriodicalIF":1.6,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Which symmetry group for elementary particles with an electric charge today and in the past?","authors":"G. de Saxcé","doi":"10.1016/j.geomphys.2025.105491","DOIUrl":"10.1016/j.geomphys.2025.105491","url":null,"abstract":"<div><div>In this paper, we revisit the Kaluza-Klein theory from the perspective of the classification of elementary particles based on the coadjoint orbit method. The key conjecture is to consider the electric charge as an extra momentum on an equal footing with the mass and the linear momentum. We study the momentum map of the corresponding symmetry group <span><math><msub><mrow><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub></math></span> which conserves the hyperbolic metric. We show that the electric charge is not an invariant, <em>i.e.</em> it depends on the reference frame, which is in contradiction with the experimental observations. In other words, it is not the symmetry group of the Universe today as we know it. To avert this paradox, we scale the fifth coordinate and consider the limit in which the cylinder radius <em>ω</em> vanishes. For the corresponding group <span><math><msub><mrow><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msub></math></span>, the charge is an invariant and therefore independent of the frame of reference and the observer. On this basis, we propose a cosmological scenario in which the elementary particles of the early Universe are classified from the momenta of the group <span><math><msub><mrow><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub></math></span>, with the three former dimensions inflating quickly while the fifth one shrinks, leading to a 4D era in which as today the particles are characterized by the momenta of the group <span><math><msub><mrow><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msub></math></span>. By this mechanism, the elementary particles can acquire electric charge as a by-product of the <span><math><mn>4</mn><mo>+</mo><mn>1</mn></math></span> symmetry breaking of the Universe. This work opens the way for the geometric quantization of charged elementary particles. We construct the corresponding <span><math><msub><mrow><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msub></math></span>-connections as a pullback connection over the space-time. Requiring that the linear 5-momentum is parallel-transported, we recover the conservation of the charge and the equation of motion with the Lorentz force. We revisit the variational relativity and obtain the field equations for both the gravitation and electromagnetic interactions with coupling terms which are negligible in the Newtonian approximation, allowing recovery of the Maxwell equations.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105491"},"PeriodicalIF":1.6,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-Whittaker supermodules for the super Schrödinger algebra","authors":"Xinyue Wang ,&nbsp;Liangyun Chen ,&nbsp;Yao Ma","doi":"10.1016/j.geomphys.2025.105490","DOIUrl":"10.1016/j.geomphys.2025.105490","url":null,"abstract":"<div><div>In this paper, let <span><math><mi>S</mi></math></span> denote the <span><math><mi>N</mi><mo>=</mo><mn>1</mn></math></span> super Schrödinger algebra in <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-dimensional spacetime. We first define the (universal) quasi-Whittaker supermodules and quasi-Whittaker vectors over <span><math><mi>S</mi></math></span>. Then we prove that any simple <span><math><mi>S</mi></math></span>-supermodule is a quasi-Whittaker supermodule if and only if it is a locally finite supermodule over the Heisenberg subalgebra of <span><math><mi>S</mi></math></span>. We also describe all quasi-Whittaker vectors of the universal quasi-Whittaker supermodule and its quotient module. At last, we give the classification of simple quasi-Whittaker <span><math><mi>S</mi></math></span>-supermodules.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105490"},"PeriodicalIF":1.6,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Revisit Hamiltonian S1-manifolds of dimension 6 with 4 fixed points","authors":"Hui Li","doi":"10.1016/j.geomphys.2025.105489","DOIUrl":"10.1016/j.geomphys.2025.105489","url":null,"abstract":"<div><div>If the circle acts in a Hamiltonian way on a compact symplectic manifold of dimension 2<em>n</em>, then there are at least <span><math><mi>n</mi><mo>+</mo><mn>1</mn></math></span> fixed points. The case that there are exactly <span><math><mi>n</mi><mo>+</mo><mn>1</mn></math></span> isolated fixed points has its importance due to various reasons. Besides dimension 2 with 2 fixed points, and dimension 4 with 3 fixed points, which are known, the next interesting case is dimension 6 with 4 fixed points, for which the integral cohomology ring and the total Chern class of the manifold, and the sets of weights of the circle action at the fixed points are classified by Tolman. In this note, we use a new different argument to prove Tolman's results for the dimension 6 with 4 fixed points case. We observe that the integral cohomology ring of the manifold has a nice basis in terms of the moment map values of the fixed points, and the largest weight between two fixed points is nicely related to the first Chern class of the manifold. We will use these ingredients to determine the sets of weights of the circle action at the fixed points, and moreover to determine the global invariants the integral cohomology ring and total Chern class of the manifold. The idea allows a direct approach of the problem, and the argument is short and easy to follow.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105489"},"PeriodicalIF":1.6,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local and 2-local automorphisms of null-filiform and filiform Zinbiel algebras","authors":"F.N. Arzikulov ,&nbsp;I.A. Karimjanov ,&nbsp;S.M. Umrzaqov","doi":"10.1016/j.geomphys.2025.105487","DOIUrl":"10.1016/j.geomphys.2025.105487","url":null,"abstract":"<div><div>In the present paper we give a description of local automorphisms of null-filiform and filiform Zinbiel algebras. It turns out, every such Zinbiel algebra has a local automorphism that is not an automorphism. Theorems on the description of 2-local automorphisms of null-filiform and filiform Zinbiel algebras are also proved.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105487"},"PeriodicalIF":1.6,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Noncommutative distances on graphs: An explicit approach via Birkhoff-James orthogonality","authors":"Pierre Clare ,&nbsp;Chi-Kwong Li ,&nbsp;Edward Poon ,&nbsp;Eric Swartz","doi":"10.1016/j.geomphys.2025.105483","DOIUrl":"10.1016/j.geomphys.2025.105483","url":null,"abstract":"<div><div>We study the problem of calculating noncommutative distances on graphs, using techniques from linear algebra, specifically, Birkhoff-James orthogonality. A complete characterization of the solutions is obtained in the case when the underlying graph is a path.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105483"},"PeriodicalIF":1.6,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discrete Lorentz surfaces and s-embeddings I: Isothermic surfaces","authors":"Niklas Christoph Affolter ,&nbsp;Felix Dellinger ,&nbsp;Christian Müller ,&nbsp;Denis Polly ,&nbsp;Nina Smeenk","doi":"10.1016/j.geomphys.2025.105482","DOIUrl":"10.1016/j.geomphys.2025.105482","url":null,"abstract":"<div><div>S-embeddings were introduced by Chelkak as a tool to study the conformal invariance of the thermodynamic limit of the Ising model. Moreover, Chelkak, Laslier and Russkikh introduced a lift of s-embeddings to Lorentz space, and showed that in the limit the lift converges to a maximal surface. They posed the question whether there are s-embeddings that lift to maximal surfaces already at the discrete level, before taking the limit. This paper is the first in a two paper series, in which we answer that question in the positive. In this paper we introduce a correspondence between s-embeddings (incircular nets) and congruences of touching Lorentz spheres. This geometric interpretation of s-embeddings enables us to apply the tools of discrete differential geometry. We identify a subclass of s-embeddings – isothermic s-embeddings – that lift to (discrete) S-isothermic surfaces, which were introduced by Bobenko and Pinkall. S-isothermic surfaces are the key component that will allow us to obtain discrete maximal surfaces in the follow-up paper. Moreover, we show here that the Ising weights of an isothermic s-embedding are in a subvariety.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105482"},"PeriodicalIF":1.6,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143695913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The nonholonomic bracket on contact mechanical systems","authors":"Víctor M. Jiménez ,&nbsp;Manuel de León","doi":"10.1016/j.geomphys.2025.105484","DOIUrl":"10.1016/j.geomphys.2025.105484","url":null,"abstract":"<div><div>In this paper, we study contact nonholonomic mechanical systems. The contribution of the paper could be divided into two blocks. Firstly, we present a general framework for contact constrained dynamics in such a way that the constraints are geometrically described by a submanifold of the contact manifold and the reaction forces are given by a distribution along the constraint submanifold. In this framework, we describe the constrained differential equations, examine the conditions for the existence and uniqueness of solutions of these equations, and construct two different brackets of functions which describe the evolution of the system. We also prove that nonholonomic contact Lagrangian systems are particular cases of the above general framework. In addition, this general framework permits us to develop the Hamiltonian counterpart and, in this setting, we present the second main contribution of the paper: the construction of another bracket, which is a natural extension of that defined by R.J. Eden, but now it is an almost Jacobi bracket since it does not satisfy the Leibniz rule.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105484"},"PeriodicalIF":1.6,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143632086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topological and numerical approaches to surface transformations","authors":"Selcuk Koyuncu ,&nbsp;Ritvik Shah ,&nbsp;Cenap Ozel","doi":"10.1016/j.geomphys.2025.105472","DOIUrl":"10.1016/j.geomphys.2025.105472","url":null,"abstract":"<div><div>Transforming a set of points between surfaces in three-dimensional space while preserving certain relative geometric constraints such as arc-lengths and angles from a reference point is a nontrivial task, especially in applications like swarm robotics. Although local differential and numerical methods can approximate these transformations, global properties often obstruct perfectly preserving all desired metrics. In this paper, we introduce a topological and geometric framework for understanding such transformations. We introduce a notion of “distortion” that quantifies how closely a transformation preserves prescribed arc-lengths and angular relationships originating from a point and show that if two surfaces differ topologically, there is a positive lower bound on the minimal distortion achievable by any continuous transformation. In the last section, we explore two numerical approaches and include several numerical examples.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105472"},"PeriodicalIF":1.6,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Double complexes for configuration spaces and hypergraphs on manifolds","authors":"Shiquan Ren","doi":"10.1016/j.geomphys.2025.105486","DOIUrl":"10.1016/j.geomphys.2025.105486","url":null,"abstract":"<div><div>In this paper, we consider hypergraphs whose vertices are distinct points moving smoothly on a Riemannian manifold <em>M</em>. We take these hypergraphs as graded submanifolds of configuration spaces. We construct double complexes of differential forms on configuration spaces. Then we construct double complexes of differential forms on hypergraphs which are sub-double complexes of the double complex for the ambient configuration space. Among these double complexes for hypergraphs, the infimum double complex and the supremum double complex are quasi-isomorphic concerning the boundary maps induced from vertex deletion of the hyperedges. In particular, all the double complexes are identical if the hypergraph is a Δ-submanifold of the ambient configuration space.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105486"},"PeriodicalIF":1.6,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}