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Manifolds of vortex loops as coadjoint orbits 作为伴随轨道的涡环流形
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-10-01 DOI: 10.1016/j.difgeo.2025.102300
Ioana Ciuclea, Cornelia Vizman
{"title":"Manifolds of vortex loops as coadjoint orbits","authors":"Ioana Ciuclea,&nbsp;Cornelia Vizman","doi":"10.1016/j.difgeo.2025.102300","DOIUrl":"10.1016/j.difgeo.2025.102300","url":null,"abstract":"<div><div>We study a class of coadjoint orbits of the area preserving diffeomorphism group of the plane consisting of vortex loops, namely closed curves in the plane decorated with one-forms (vorticity densities) allowed to have zeros.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102300"},"PeriodicalIF":0.7,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quaternionic projective invariance of the k-Cauchy-Fueter complex and applications I k-Cauchy-Fueter复合体的四元数射影不变性及其应用[j]
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-26 DOI: 10.1016/j.difgeo.2025.102299
Wei Wang
{"title":"Quaternionic projective invariance of the k-Cauchy-Fueter complex and applications I","authors":"Wei Wang","doi":"10.1016/j.difgeo.2025.102299","DOIUrl":"10.1016/j.difgeo.2025.102299","url":null,"abstract":"<div><div>The <em>k</em>-Cauchy-Fueter complex in quaternionic analysis is the counterpart of the Dolbeault complex in complex analysis. In this paper, we find the explicit transformation formula of these complexes under <span><math><mrow><mi>SL</mi></mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>H</mi><mo>)</mo></math></span>, which acts on <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> as quaternionic fractional linear transformations. These transformation formulae have several interesting applications to <em>k</em>-regular functions, the quaternionic counterpart of holomorphic functions, and geometry of domains. They allow us to construct the <em>k</em>-Cauchy-Fueter complex over locally quaternionic projective flat manifolds explicitly and introduce various notions of pluripotential theory on this kind of manifolds. We also construct a quaternionic projectively invariant operator from the quaternionic Monge-Ampère operator, which can be used to find projectively invariant defining density of a domain, generalizing Fefferman's construction in complex analysis.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102299"},"PeriodicalIF":0.7,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rotational surfaces with prescribed curvatures 具有规定曲率的旋转曲面
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-25 DOI: 10.1016/j.difgeo.2025.102298
Paula Carretero , Ildefonso Castro
{"title":"Rotational surfaces with prescribed curvatures","authors":"Paula Carretero ,&nbsp;Ildefonso Castro","doi":"10.1016/j.difgeo.2025.102298","DOIUrl":"10.1016/j.difgeo.2025.102298","url":null,"abstract":"<div><div>We solve the problem of prescribing different types of curvatures (principal, mean or Gaussian) on rotational surfaces in terms of arbitrary continuous functions depending on the distance from the surface to the axis of revolution. In this line, we get the complete explicit classification of the rotational surfaces with mean or Gauss curvature inversely proportional to the distance from the surface to the axis of revolution. We also provide new uniqueness results on some well known surfaces, such as the catenoid or the torus of revolution, and others less well known but equally interesting for their physical applications, such as the Mylar balloon or the Flamm's paraboloid.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102298"},"PeriodicalIF":0.7,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of non-diagonal Einstein metrics on homogeneous spaces H × H/ΔK 齐次空间H × H/ΔK上非对角爱因斯坦度量的稳定性
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-22 DOI: 10.1016/j.difgeo.2025.102295
Valeria Gutiérrez
{"title":"Stability of non-diagonal Einstein metrics on homogeneous spaces H × H/ΔK","authors":"Valeria Gutiérrez","doi":"10.1016/j.difgeo.2025.102295","DOIUrl":"10.1016/j.difgeo.2025.102295","url":null,"abstract":"<div><div>We consider the homogeneous space <span><math><mi>M</mi><mo>=</mo><mi>H</mi><mo>×</mo><mi>H</mi><mo>/</mo><mi>Δ</mi><mi>K</mi></math></span>, where <span><math><mi>H</mi><mo>/</mo><mi>K</mi></math></span> is an irreducible symmetric space and Δ<em>K</em> denotes diagonal embedding. Recently, Lauret and Will provided a complete classification of <span><math><mi>H</mi><mo>×</mo><mi>H</mi></math></span>-invariant Einstein metrics on M. They obtained that there is always at least one non-diagonal Einstein metric on <em>M</em>, and in some cases, diagonal Einstein metrics also exist. We give a formula for the scalar curvature of a subset of <span><math><mi>H</mi><mo>×</mo><mi>H</mi></math></span>-invariant metrics and study the stability of non-diagonal Einstein metrics on <em>M</em> with respect to the Hilbert action, obtaining that these metrics are unstable with different coindices for all homogeneous spaces <em>M</em>.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102295"},"PeriodicalIF":0.7,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized weakly-Weyl Finsler metrics: A generalized approach to Sakaguchi's theorem 广义弱weyl - Finsler度量：Sakaguchi定理的广义方法
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-19 DOI: 10.1016/j.difgeo.2025.102297
Nasrin Sadeghzadeh, Meshkat Yavari
{"title":"Generalized weakly-Weyl Finsler metrics: A generalized approach to Sakaguchi's theorem","authors":"Nasrin Sadeghzadeh,&nbsp;Meshkat Yavari","doi":"10.1016/j.difgeo.2025.102297","DOIUrl":"10.1016/j.difgeo.2025.102297","url":null,"abstract":"<div><div>The development of projective invariant Weyl metrics in this paper offers a fresh perspective, as we establish the characteristics of both weakly-Weyl and generalized weakly-Weyl Finsler metrics. We thoroughly examine the connections between these metrics and various projective invariants, highlighting their significance in the context of generalized Sakaguchi's Theorem, which states that every Finsler metric of scalar flag curvature is a GDW-metric. Additionally, we introduce several illustrative examples pertaining to this new class of projective invariant Finsler metrics. Specifically, we explore the category of weakly-Weyl spherically symmetric Finsler metrics in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Importantly, we demonstrate that the two classes weakly-Weyl and <em>W</em>-quadratic spherically symmetric Finsler metrics in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> are equivalent.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102297"},"PeriodicalIF":0.7,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the real projective blowup of Poisson structures 泊松结构的实投影爆破
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-19 DOI: 10.1016/j.difgeo.2025.102293
Andreas Schüßler
{"title":"On the real projective blowup of Poisson structures","authors":"Andreas Schüßler","doi":"10.1016/j.difgeo.2025.102293","DOIUrl":"10.1016/j.difgeo.2025.102293","url":null,"abstract":"<div><div>We give a proof in the context of smooth differential geometry of Polishchuk's theorem from 1997, in which he established under which conditions, given a Poisson scheme <em>M</em> and a Poisson subscheme <em>N</em>, the Poisson structure lifts to the blowup of <em>M</em> along <em>N</em>.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102293"},"PeriodicalIF":0.7,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on pullbacks and blowups of Lie algebroids, singular foliations, and Dirac structures 李代数、奇叶和狄拉克结构的回调和膨胀注解
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-18 DOI: 10.1016/j.difgeo.2025.102296
Andreas Schüßler, Marco Zambon
{"title":"A note on pullbacks and blowups of Lie algebroids, singular foliations, and Dirac structures","authors":"Andreas Schüßler,&nbsp;Marco Zambon","doi":"10.1016/j.difgeo.2025.102296","DOIUrl":"10.1016/j.difgeo.2025.102296","url":null,"abstract":"<div><div>Lie algebroids, singular foliations, and Dirac structures are closely related objects. We examine the relation between their pullbacks under maps satisfying a constant rank or transversality assumption. A special case is given by blowdown maps. In that case, we also establish the relation between the blowup of a Lie algebroid and its singular foliation.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102296"},"PeriodicalIF":0.7,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-naturally reductive Einstein metrics on SO(n) SO(n)上的非自然约简爱因斯坦度量
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-16 DOI: 10.1016/j.difgeo.2025.102294
Ming Wu , Ju Tan , Na Xu
{"title":"Non-naturally reductive Einstein metrics on SO(n)","authors":"Ming Wu ,&nbsp;Ju Tan ,&nbsp;Na Xu","doi":"10.1016/j.difgeo.2025.102294","DOIUrl":"10.1016/j.difgeo.2025.102294","url":null,"abstract":"<div><div>In this article, we obtain that the compact simple Lie group <span><math><mi>S</mi><mi>O</mi><mo>(</mo><mn>4</mn><mi>k</mi><mo>+</mo><mn>3</mn><mo>)</mo><mo>(</mo><mi>k</mi><mo>≥</mo><mn>8</mn><mo>)</mo></math></span> admits at least two new non-naturally reductive <span><math><mi>A</mi><mi>d</mi><mo>(</mo><mi>S</mi><mi>O</mi><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>×</mo><mi>S</mi><mi>O</mi><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>×</mo><mi>S</mi><mi>O</mi><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>×</mo><mi>S</mi><mi>O</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>)</mo></math></span>-invariant Einstein metrics, and the compact simple Lie group <span><math><mi>S</mi><mi>O</mi><mo>(</mo><mn>4</mn><mi>k</mi><mo>+</mo><mn>6</mn><mo>)</mo><mo>(</mo><mi>k</mi><mo>≥</mo><mn>11</mn><mo>)</mo></math></span> admits at least two new non-naturally reductive <span><math><mi>A</mi><mi>d</mi><mo>(</mo><mi>S</mi><mi>O</mi><mo>(</mo><mi>k</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>×</mo><mi>S</mi><mi>O</mi><mo>(</mo><mi>k</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>×</mo><mi>S</mi><mi>O</mi><mo>(</mo><mi>k</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>×</mo><mi>S</mi><mi>O</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>)</mo></math></span>-invariant Einstein metrics. Furthermore, we explore the isometry problem for these Einstein metrics. Finally, we prove that there are at least two families of non-naturally reductive invariant Einstein-Randers metrics on <span><math><mi>S</mi><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>(</mo><mi>n</mi><mo>≥</mo><mn>35</mn><mo>)</mo></math></span> and <span><math><mi>S</mi><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>(</mo><mi>n</mi><mo>≥</mo><mn>50</mn><mo>)</mo></math></span> respectively.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102294"},"PeriodicalIF":0.7,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Vector fields and derivations on differentiable stacks 可微堆栈上的向量场和导数
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-16 DOI: 10.1016/j.difgeo.2025.102292
Juan Sebastián Herrera-Carmona , Cristian Ortiz , James Waldron
{"title":"Vector fields and derivations on differentiable stacks","authors":"Juan Sebastián Herrera-Carmona ,&nbsp;Cristian Ortiz ,&nbsp;James Waldron","doi":"10.1016/j.difgeo.2025.102292","DOIUrl":"10.1016/j.difgeo.2025.102292","url":null,"abstract":"<div><div>We introduce and study module structures on both the dgla of multiplicative vector fields and the graded algebra of functions on Lie groupoids. We show that there is an associated structure of a graded Lie-Rinehart algebra on the vector fields of a differentiable stack over its smooth functions that is Morita invariant in an appropriate sense. Furthermore, we show that associated Van-Est type maps are compatible with those module structures. We also present several examples.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102292"},"PeriodicalIF":0.7,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalised spinr structures on homogeneous spaces 齐次空间上的广义旋旋结构
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-12 DOI: 10.1016/j.difgeo.2025.102291
Diego Artacho, Marie-Amélie Lawn
{"title":"Generalised spinr structures on homogeneous spaces","authors":"Diego Artacho,&nbsp;Marie-Amélie Lawn","doi":"10.1016/j.difgeo.2025.102291","DOIUrl":"10.1016/j.difgeo.2025.102291","url":null,"abstract":"<div><div>Spinorial methods have proven to be a powerful tool to study geometric properties of spin manifolds. Our aim is to continue the spinorial study of manifolds that are not necessarily spin. We introduce and study the notion of <em>G</em>-invariance of spin<sup><em>r</em></sup> structures on a manifold <em>M</em> equipped with an action of a Lie group <em>G</em>. For the case when <em>M</em> is a homogeneous <em>G</em>-space, we prove a classification result of these invariant structures in terms of the isotropy representation. As an example, we study the invariant spin<sup><em>r</em></sup> structures for all the homogeneous realisations of the spheres.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102291"},"PeriodicalIF":0.7,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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