Differential Geometry and its Applications最新文献

{"title":"On the scalar curvature of Kropina metrics II","authors":"Hongmei Zhu ,&nbsp;Lumin Song","doi":"10.1016/j.difgeo.2025.102322","DOIUrl":"10.1016/j.difgeo.2025.102322","url":null,"abstract":"<div><div>In this paper, we study two different kinds of scalar curvature in Finsler geometry, which are defined by two different kinds of Ricci curvature tensor. For Kropina metrics, we show that they are equivalent among weakly isotropic scalar curvature, isotropic scalar curvature, weakly isotropic Ricci curvature tensor, weakly isotropic Ricci curvature, isotropic Ricci curvature tensor and isotropic Ricci curvature.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"102 ","pages":"Article 102322"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145748054","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}

{"title":"Riemannian metric representatives of the Stiefel-Whitney classes","authors":"Santiago R. Simanca","doi":"10.1016/j.difgeo.2025.102325","DOIUrl":"10.1016/j.difgeo.2025.102325","url":null,"abstract":"&lt;div&gt;&lt;div&gt;If &lt;em&gt;M&lt;/em&gt; is a closed manifold, and &lt;em&gt;K&lt;/em&gt; is a smooth triangulation of &lt;em&gt;M&lt;/em&gt;, Whitney proved that all of the Stiefel-Whitney classes are specified as cochains on the dual cell complex &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; assigning the value 1 mod 2 to each dual cell. We provide the pair &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with an arbitrary Riemannian metric &lt;em&gt;g&lt;/em&gt;, and use Whitney's criteria to show that there are associated representatives of all the Stiefel-Whitney classes &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. The representative of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is determined by &lt;span&gt;&lt;math&gt;&lt;mi&gt;det&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, the &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;s computed in a frame that is locally defined at each dual 1-cell; the representatives of the even classes &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; are determined by the Chern-Gauss-Bonnet density 2&lt;em&gt;k&lt;/em&gt;-form of locally defined totally geodesic oriented 2&lt;em&gt;k&lt;/em&gt; manifolds with boundary associated to each dual 2&lt;em&gt;k&lt;/em&gt;-cell; and the representatives of the odd classes &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; are determined by the hypersurface area form of the boundary sphere of a locally defined totally geodesic oriented &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; manifold with boundary associated to each dual &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;-cell. If &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is Hermitian, we prove that the metric representative of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; so obtained is the &lt;span&gt;&lt;math&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; reduction of the &lt;em&gt;k&lt;/em&gt;th Chern class &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; induced by the coefficient homomorphism, and that the metric representative of any odd degree class &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/m","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"102 ","pages":"Article 102325"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840301","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}

{"title":"Classification of conformal minimal immersions from S2 to G(2,N;C) with parallel second fundamental form","authors":"Xiaoxiang Jiao ,&nbsp;Mingyan Li","doi":"10.1016/j.difgeo.2025.102312","DOIUrl":"10.1016/j.difgeo.2025.102312","url":null,"abstract":"<div><div>In this paper, we determine all conformal minimal immersions of 2-spheres in complex Grassmann manifold <span><math><mi>G</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>N</mi><mo>;</mo><mi>C</mi><mo>)</mo></math></span> with parallel second fundamental form.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102312"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145623137","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}

{"title":"Studies of the torsion in the homology of Oeljeklaus–Toma manifolds","authors":"Dung Phuong Phan ,&nbsp;Tuan Anh Bui ,&nbsp;Alexander D. Rahm","doi":"10.1016/j.difgeo.2025.102304","DOIUrl":"10.1016/j.difgeo.2025.102304","url":null,"abstract":"<div><div>This article investigates the torsion homology behaviour in towers of Oeljeklaus–Toma (OT) manifolds. This adapts an idea of Silver–Williams from knot theory to OT manifolds and extends it to higher degree homology groups.</div><div>In the case of surfaces, i.e. Inoue surfaces of type <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span>, the torsion grows exponentially in both <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> (as was established by Bräunling) and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> (our result) according to a parameter which already plays a role in Inoue's classical paper, and we obtain that the torsion vanishes in all higher degrees. This motivates our presented machine calculations for OT manifolds of one dimension higher.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102304"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320641","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}

{"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":"2025-12-01","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}

{"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":"2025-12-01","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}

{"title":"Deformations of cohesive modules on compact complex manifolds","authors":"Zhaoting Wei","doi":"10.1016/j.difgeo.2025.102306","DOIUrl":"10.1016/j.difgeo.2025.102306","url":null,"abstract":"<div><div>Cohesive modules give a dg-enhancement of the bounded derived category of coherent sheaves on a complex manifold via superconnections. In this paper we discuss the deformation theory of cohesive modules on compact complex manifolds. This generalizes the deformation theory of holomorphic vector bundles and coherent sheaves. We also develop the theory of Kuranishi maps and obstructions of deformations of cohesive modules and give some examples of unobstructed deformations.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102306"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416379","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}

{"title":"Rigidity and vanishing results on totally real submanifolds under Lp-integrable conditions","authors":"N.T. Dung ,&nbsp;L.G. Linh ,&nbsp;P.B. Ngan ,&nbsp;A. Upadhyay","doi":"10.1016/j.difgeo.2025.102303","DOIUrl":"10.1016/j.difgeo.2025.102303","url":null,"abstract":"<div><div>In this paper, we revise some results on rigidity and vanishing properties obtained by <em>Cuong</em> et al. in <span><span>[5]</span></span> on <em>n</em>-dimensional totally real minimal submanifolds <em>M</em> immersed in complex space forms <span><math><msup><mrow><mover><mrow><mi>M</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>c</mi><mo>)</mo></math></span>, for <span><math><mi>c</mi><mo>≤</mo><mn>0</mn></math></span>. We extend the range of <em>p</em> in their paper.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102303"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416380","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}

{"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":"2025-12-01","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}

{"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":"2025-12-01","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}