Journal of Geometry and Physics最新文献

{"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}

{"title":"Hilbert measures on orbit spaces of coregular Om-modules","authors":"Hans-Christian Herbig ,&nbsp;Christopher W. Seaton ,&nbsp;Lillian Whitesell","doi":"10.1016/j.geomphys.2025.105473","DOIUrl":"10.1016/j.geomphys.2025.105473","url":null,"abstract":"<div><div>We construct canonical measures, referred to as <em>Hilbert measures</em>, on orbit spaces of classical coregular representations of the orthogonal groups <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>. We observe that the measures have singularities along non-principal strata of the orbit space if and only if the number of copies of the defining representation of <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> is equal to <em>m</em>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105473"},"PeriodicalIF":1.6,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645118","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":"Tame deformations of highly singular function germs","authors":"Cezar Joiţa ,&nbsp;Matteo Stockinger ,&nbsp;Mihai Tibăr","doi":"10.1016/j.geomphys.2025.105471","DOIUrl":"10.1016/j.geomphys.2025.105471","url":null,"abstract":"<div><div>We give analytic and algebraic conditions under which a deformation of real analytic functions with non-isolated singular locus is a deformation with fibre constancy.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105471"},"PeriodicalIF":1.6,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562354","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":"Field theory via higher geometry I: Smooth sets of fields","authors":"Grigorios Giotopoulos ,&nbsp;Hisham Sati","doi":"10.1016/j.geomphys.2025.105462","DOIUrl":"10.1016/j.geomphys.2025.105462","url":null,"abstract":"<div><div>Most modern theoretical considerations of the physical world suggest that nature is at a minimum: (1) field-theoretic, (2) smooth, (3) local, (4) gauged, (5) containing fermions, and last but not least: (6) non-perturbative. Tautologous as this may sound to experts of the field, it is remarkable that the mathematical notion of geometry which reflects <em>all</em> of these aspects – namely, as we will explain: “<em>supergeometric homotopy theory</em>” – has received little attention even by mathematicians and remains unknown to most physicists. Elaborate algebraic machinery is known for <em>perturbative</em> field theories both at the classical and quantum level, but in order to tackle the deep open questions of the subject, these will need to be lifted to a global geometry of physics. Prior to considering any notion of non-perturbative quantization procedure, by necessity, this must first be accomplished at the classical and pre-quantum level.</div><div>Our aim in this series is, first, to introduce inclined physicists to this theory, second to fill mathematical gaps in the existing literature, and finally to rigorously develop the full power of supergeometric homotopy theory and apply it to the analysis of fermionic (not <em>necessarily</em> super-symmetric) field theories. Secondarily, this will also lead to a streamlined and rigorous perspective of the type that we hope would also be desirable to mathematicians.</div><div>In this first part, we explain how classical bosonic Lagrangian field theory (variational Euler-Lagrange theory) finds a natural home in the “topos of smooth sets”, thereby neatly setting the scene for the higher supergeometry discussed in later parts of the series. This introductory material will be largely known to a few experts but has never been comprehensively laid out before. A key technical point we make is to regard jet bundle geometry systematically in smooth sets instead of just its subcategories of diffeological spaces or even Fréchet manifolds – or worse simply as a formal object. Besides being more transparent and powerful, it is only on this backdrop that a reasonable supergeometric jet geometry exists, needed for satisfactory discussion of any field theory with fermions.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105462"},"PeriodicalIF":1.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562276","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":"Spinors and the Descartes circle theorem","authors":"Daniel V. Mathews ,&nbsp;Orion Zymaris","doi":"10.1016/j.geomphys.2025.105458","DOIUrl":"10.1016/j.geomphys.2025.105458","url":null,"abstract":"<div><div>The classic Descartes circle theorem relates the curvatures of four mutually externally tangent circles, three “petal” circles around the exterior of a central circle, forming a “3-flower” configuration. We generalise this theorem to the case of an “<em>n</em>-flower”, consisting of <em>n</em> tangent circles around the exterior of a central circle, and give an explicit equation satisfied by their curvatures. The proof uses a spinorial description of horospheres in hyperbolic geometry.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"212 ","pages":"Article 105458"},"PeriodicalIF":1.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511062","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":"Rigidity results for compact biconservative hypersurfaces in space forms","authors":"Ştefan Andronic ,&nbsp;Aykut Kayhan","doi":"10.1016/j.geomphys.2025.105460","DOIUrl":"10.1016/j.geomphys.2025.105460","url":null,"abstract":"<div><div>In this paper we present alternative proofs for two known rigidity results concerning non-negatively curved compact biconservative hypersurfaces in space forms. Further, we prove some new rigidity results by replacing the hypothesis of non-negative sectional curvature with some estimates of the squared norm of the shape operator.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"212 ","pages":"Article 105460"},"PeriodicalIF":1.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511061","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 recursion and variations of spectral curves for twisted Higgs bundles","authors":"Christopher Mahadeo ,&nbsp;Steven Rayan","doi":"10.1016/j.geomphys.2025.105459","DOIUrl":"10.1016/j.geomphys.2025.105459","url":null,"abstract":"<div><div>Prior works relating meromorphic Higgs bundles to topological recursion, in particular those of Dumitrescu-Mulase, have considered non-singular models that allow the recursion to be carried out on a smooth Riemann surface. We start from an <span><math><mi>L</mi></math></span>-twisted Higgs bundle for some fixed holomorphic line bundle <span><math><mi>L</mi></math></span> on the surface. We decorate the Higgs bundle with the choice of a section <em>s</em> of <span><math><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>⊗</mo><mi>L</mi></math></span>, where <em>K</em> is the canonical line bundle, and then encode this data as a <em>b</em>-structure on the base Riemann surface which lifts to the associated Hitchin spectral curve. We then propose a so-called twisted topological recursion on the spectral curve, after which the corresponding Eynard-Orantin differentials live in a twisted cotangent bundle. This formulation retains, and interacts explicitly with, the singular structure of the original meromorphic setting — equivalently, the zero divisor of <em>s</em> — while performing the recursion. Finally, we show that the <span><math><mi>g</mi><mo>=</mo><mn>0</mn></math></span> twisted Eynard-Orantin differentials compute the Taylor expansion of the period matrix of the spectral curve, mirroring a result of Baraglia-Huang for ordinary Higgs bundles and topological recursion. Starting from the spectral curve as a polynomial form in an affine coordinate rather than a Higgs bundle, our result implies that, under certain conditions on <em>s</em>, the expansion is independent of the ambient space <span><math><mtext>Tot</mtext><mo>(</mo><mi>L</mi><mo>)</mo></math></span> in which the curve is interpreted to reside. While our focus is almost exclusively geometric, we include some preliminary thoughts on connections to questions in theoretical condensed matter physics.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105459"},"PeriodicalIF":1.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601619","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":"Quasi-Einstein structures on f-associated standard static space-time","authors":"Sameh Shenawy ,&nbsp;Uday Chand De ,&nbsp;Ibrahim Mandour ,&nbsp;Nasser Bin Turki","doi":"10.1016/j.geomphys.2025.105463","DOIUrl":"10.1016/j.geomphys.2025.105463","url":null,"abstract":"<div><div>In a generalized quasi-Einstein <em>f</em>-associated standard static space-time, the Laplacian Δ of the warping function <em>f</em> adheres to the Laplacian equation. The Ricci tensor of the base manifold satisfies the generalized Ricci-Hessian equation. The base manifold is shown to be quasi-Einstein if the Hessian <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>f</mi></mrow></msup></math></span> of the warping function <em>f</em> is proportional to the metric tensor, and it is proven to be a generalized quasi-Einstein manifold if <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>f</mi></mrow></msup></math></span> takes on the form of a perfect fluid tensor. The scalar curvature of both the space-time and its base manifold are provided. The Ricci curvature of the base manifold, the Laplacian of the warping function and the scalar curvature of the base manifold in a quasi-Einstein <em>f</em>-associated SSST are described in two scenarios: when the generator is space-like and when it is time-like. In the first scenario, it is demonstrated that the space-time is Ricci simple and the warping function remains constant if the base manifold is constant. In a generalized quasi-Einstein standard static space-time, the base manifold is a generalized quasi-Einstein manifold if the Hessian <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>f</mi></mrow></msup></math></span> is proportional the metric tensor. A specific example of an <em>f</em>-associated standard static space-time is also provided. The equation of state takes the form <span><math><mi>p</mi><mo>=</mo><mi>w</mi><mi>σ</mi></math></span> where <em>w</em> ranges from −1 to 0, representing a transition from dark energy-dominated space-times to non-relativistic, matter-dominated ones.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"212 ","pages":"Article 105463"},"PeriodicalIF":1.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534128","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":"Cocommutative connected vertex (operator) bialgebras","authors":"Yukun Xiao ,&nbsp;Jianzhi Han","doi":"10.1016/j.geomphys.2025.105461","DOIUrl":"10.1016/j.geomphys.2025.105461","url":null,"abstract":"<div><div>In this paper, by the equivalence between the category of Lie conformal algebras and the category of cocommutative connected vertex bialgebras, which was obtained in <span><span>[8]</span></span>, we classify simple objects in the latter category. We introduce the notion of Lie conformal operator algebra and the notion of vertex operator bialgebra. And it is shown that the category of Lie conformal operator algebras and the category of cocommutative connected vertex operator bialgebras are equivalent.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"212 ","pages":"Article 105461"},"PeriodicalIF":1.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510452","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}